Geometry First Semester Practice Final (cont)

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Geometry First Semester Practice Final (cont)"

Transcription

1 49. Determine the width of the river, AE, if A. 6.6 yards. 10 yards C yards D. 15 yards Geometry First Semester Practice Final (cont) 50. In the similar triangles shown below, what is the value of x? A C. 18 D J K 15 L 20 x M 51.. Determine the length of the longest side of. A A C. 648 D C 216 Z N 576 X Y 52. Which additional piece of information would prove that? A. NM = 18 N K. LM = 18 C. NM = D. LM = 10 L M I 10 J 53. For,. Find the length of A C. 10 D. 20 X (cont) Q 6 Y R 14 7 Z Geometry 101

2 Geometry First Semester Practice Final (cont) 54. Lines l, m, and n are parallel. Determine the value of x. A C. 8.5 D Determine the value of x. A C. 20 D Determine the length of. A C. 52 D A D 12 x C 4 N 15 M 6 (2x + 1) x 25 l m n L A (3x 5) C Geometry 102

3 Unit 7 Objective 0 Determine the value of the missing angle in each of the figures below: NOTE: DIAGRAMS ARE NOT DRAWN TO SCALE (cont) Geometry 103

4 Unit 7 Objective 0 (cont) Determine the value of the missing angle in each of the figures below: NOTE: DIAGRAMS ARE NOT DRAWN TO SCALE Geometry 104

5 Geometry Unit 7 1. Apply the Pythagorean Theorem (Section 7.1) 2. Use the converse of the Pythagorean Theorem (Section 7.2) 3. Use Similar Right Triangles (Section 7.3) 4. Special Right Triangles (Section 7.4) 5. Apply the Tangent Ratio (Section 7.5) 6. Apply the Sine and Cosine Ratios (Section 7.6) 7. Solve Right Triangles (Section 7.7) Review Geometry 105

6 Unit 7 Trig Worksheet 1 Remember SOH CAH TOA sin = cos = tan = C Example 1: Find the value of cos A tan 5 4 Solution: cos A tan C = 3 = = Example 2: Find the value of sin 2 A Solution: sin 2 A = (sin A) (sin A) = C 5 A Homework = = Use shown to find the values in problems N 6 L 8 1. sin L cos L 2. tan N sin L 3. cos L 2 tan N M 4. tan 2 L cos 2 L 6. sin 2 L + cos 2 L (cont) Geometry 106

7 Unit 7 Trig Worksheet 1 (cont) Use the triangle shown to find the values in problems sin A cos 8. tan sin A sin 2 A cos 2 A 11. tan C 4 A Geometry 107

8 Notes: Unit 7 Trig Worksheet 2 Let s review the formulas for sin, cos, tan. sin = cos = tan = We have been finding these values using triangles with numbers. C Example 1 Find sin A 5 4 Solution: sin A = = A 3 2 In this lesson we are not going to have numbers on the triangle. Example 2 Find sin K and tan R R P K Solution: sin K = (just put the letters of the sides) = tan R = = Example 3 Determine if the statement is true or false using the given triangle. C A Solution: A cos = C (get the trig word by itself by dividing both sides by A) cos = cos = = which is the cos formula, so True (cont) Geometry 108

9 Unit 7 Trig Worksheet 2 (cont) Homework: Using the given triangle find the requested values in problems 1-4 (Just put the letters of the sides.) U V W 1. tan W 2. sin U 3. cos U 4. tan U Draw your own right triangle and label it JKL. Use this triangle to find the values in problems 5-7. (Just put the letters of the sides.) is a right angle. 5. sin J 6. tan L 7. cos J Use the given triangle to determine whether the statements in problems 8-15 are true or false. 8. sin A = 9. cos = 10. tan A = 11. cos A = (In Problems remember to get the trig word by itself by dividing.) 12. A sin A = C 13. C tan = AC C A (In problems 14-15, put all the letters of the sides and compare the left side of the equation with the right side of the equation.) 14. sin A = cos 15. sin A = tan A cos A Geometry 109

10 Unit 7 Trig Worksheet 3 Notes: Determine whether each equation below is true or false: 1. cos 2 A + 1 = sin 2 A 2. sin 2 A + cos 2 A = 1 Solution: a) First make a right triangle. b) Put any right triangle Pythagorean numbers on your triangle. You could use 3,4,5 or 5,12,13. Let s use 3,4,5 (Remember the largest number is the hypotenuse. Also label one of the non-right angles as A c) Now, find sin A = Find cos A = A d) Now plug the fractions into each problem and see if it s true or false. 1. cos 2 A + 1 = sin 2 A 2. sin 2 A + cos 2 A = = + = = + = 1 = = 1 This is not a true equation, so the original trig problem was false. This is a true statements, so the original trig problem was true. (cont) Geometry 110

11 Unit 7 Trig Worksheet 3 (cont) Homework: Use the same triangle that we used in our note examples and give the following fraction values. 1. sin A = 2. cos A = 3. tan A = Now, using the above fraction values, determine whether each of the following is true or false. 4. sin A cos A = tan A 5. tan A cos A = sin A 6. tan A sin A = cos A 7. 1 sin 2 A = cos 2 A 8. cos 2 A sin 2 A = 1 9. cos A = tan 2 A = cos 2 A 11. tan A = 12. sin 2 A = tan 2 A cos 2 A Unit 7 Review NOTE: Diagrams are not drawn to scale. Select the correct multiple choice response: 1. The lengths of the two legs of a right triangle are 4 and 7. What is the length of the hypotenuse? A. 33. C. 65 D. 2. The lengths of the two legs of a right triangle are and 5. What is the length of the hypotenuse? A.. C. D. (cont) Geometry 111

12 Unit 7 Review (cont) 3. The length of one leg of a right triangle is and the hypotenuse is 11. Find the length of the other leg. A C. D. 4. A baseball diamond is in the shape of a square, 90 feet on each side. What is the direct distance from home plate to second base? A. 90 ft. ft C. ft D. 180 ft 5. A model rocket is launched. It rises to a point 36 feet above the ground and is 48 feet along the ground from the lift off site, as shown in the diagram. What is the length of the rocket s path in the air? A. 12 ft.. 32 ft. C. 60 ft. x D. 84 ft. Current Site of Rocket 36 ft Rocket Launch Site 48 ft 6. Which set of numbers can represent the side lengths of an obtuse triangle? A. 5, 10, 11. 3, 5, C. 3, 7, 8 D. 1, 2, 2 7. Which set of numbers below represent the lengths of the sides of a right triangle? A. 1, 2,. 5, 11, 12 C. 6, 8, D. 5, 7, 9 (cont) Geometry 112

13 Unit 7 Review (cont) A 8. Determine the length of D. A. 13. C. 36 D. 6 9 D 4 C 9. Determine the value of x. A.. x C. D Determine the value of x. A.. C. 13 D. x Determine the value of x A.. 6 C. 3 D. x Determine the height of the triangle if A = 16 cm and C = 17 cm A. cm C. cm C. 9 cm D. 15 cm A h 13. Determine the values of x and y. A. x =, y = 3. x =, y = C. x = 3, y = D. x =, y = x 60 6 y (cont) Geometry 113

14 14. Determine the value of x. Unit 7 Review (cont) A.. C. D. 40 x Which equation is equivalent to cos A =? A. x =. x = C. x = 17 cos A D. x = cos (17A) 16. Determine the value of x to the nearest tenth. A C. 7.1 D In right triangle DEF, DE = 15, EF = 36 and DF = 39. What is the cos F? A x. C. D. 18. An 80 foot support wire is attached to the top of a tower and meets the ground at a 70 angle. How tall is the tower, to the nearest foot? A. 27 ft.. 70 ft. C. 220 ft. D. 75 ft. sin 70 = 0.94 sin 20 = 0.34 cos 70 = 0.34 cos 20 = 0.94 tan 70 = 2.75 tan 20 = 0.36 (cont) Geometry 114

15 Unit 7 Review (cont) 19. A ladder is leaning against a tree and hits the tree at a point 15 feet above the ground. The ladder and the ground form a 62 angle. How far, to the nearest tenth of a foot, is the bottom of the ladder from the base of the tree? A ft.. 7 ft. C ft. D. 8 ft. sin 62 = 0.88 sin 28 = 0.47 cos 62 = 0.47 cos 28 = 0.88 tan 62 = 1.88 tan 28 = Which expression is correct? A. cos =. cos = f d C. cos = D. cos = P e 21. The angle of depression from the top of a 20-foot lighthouse to a boat in the ocean is 39. Which is closest to the distance that the boat is from the base of the lighthouse? A ft ft C ft D ft sin 39 = 0.63 sin 51 = 0.78 cos 39 = 0.78 cos 51 = 0.63 tan 39 = 0.81 tan 51 = The angle of elevation from the boy to the top of the flagpole is 35. How far (to the nearest tenth) is the boy from the base of the flagpole? A ft.. 42 ft. C. 49 ft. D ft sin 35 = 0.57 sin 55 = 0.82 cos 35 = 0.82 cos 55 = 0.57 tan 35 = 0.70 tan 55 = 1.43 Geometry 115

16 Unit 8 Objective 0 1. If possible, draw 2 obtuse triangles that are similar. Label their measurements and state whether they are similar by AA, SSS, or SAS. If not possible, state that it can t be done. 2. If possible, draw 2 obtuse triangles that are not similar. Label their measurements and state why they are not similar. 3. If possible, draw 2 scalene triangles with congruent bases that are similar. Label their measurements and state whether they are similar by AA, SSS, or SAS. If not possible, state that it can t be done. 4. If possible, draw 2 scalene triangles with congruent bases that are not similar. Label their measurements and state why they are not similar. 5. If possible, draw 2 right triangles that are similar. Label their measurements and state whether they are similar by AA, SSS, or SAS. If not possible, state that it can t be done. 6. If possible, draw 2 right triangles that are not similar. Label their measurements and state why they are not similar. 7. If possible, draw 2 isosceles triangles with congruent vertex angles that are similar. Label their measurements and state whether they are similar by AA, SSS, or SAS. If not possible, state that it can t be done. 8. If possible, draw isosceles triangles with congruent vertex angles that are not similar. Label their measurements and state why they are not similar. 9. In the figure below, determine if the value of n could be 1. Explain why or why not? n n In the figure below, determine if the value of n could be 4. Explain why or why not? n n In the figure below, determine if the value of n could be 5. Explain why or why not? n n 12. The complement of an angle is four times the measure of the angle itself. Calculate the angle and its complement. (cont) 8 Geometry 116

17 Unit 8 Objective 0 (cont) 13. The measures of the interior angles of a triangle are (6x + 6), (4x 4), and (4x + 10). Calculate the degree measures of all three angles. 14. The four sides of the figure will be folded up and taped to make an open box. What will be the volume of the box? 15. Calculate the value of x. 16. Calculate the value of x. Y 17. Supply the reasons in the proof below: Given: ; bisects Prove: Statements 1. ; bisects X Reasons W Z Geometry 117

18 Geometry Unit 8 1. Find angle measure in polygons. Interior angle sums, exterior angle sums, etc. (Section 8.1) 2. Use properties of parallelograms. (Section 8.2) 3. Show that a quadrilateral is a parallelogram. (Section 8.3) 4. Properties of rhombuses, rectangles, and squares (Section 8.4) 5. Use properties of trapezoids and kites. (Section 8.5) 6. Identify special quadrilaterals (Section 8.6) Review Geometry 118

19 Unit 8 Worksheet 2 Determine the values for the variables that make the quadrilateral a parallelogram m + 2n 2x + 4y x + 3y 16 3m + n 7 15 a b 5 a + b 9 Determine the coordinates of the point where the diagonals of the parallelogram intersect y y (5,7) (12,7) (m, n) (m + w, n) (3,4) (10,4) x x (0, 0) (w, 0) Worksheet 3 In parallelogram ACD, diagonals and intersect at point V. y theorem 8.10 we know that diagonals bisect each other so V = DV and AV = CV as shown. We also know that opposite sides are congruent in a parallelogram. Use this information and the diagram to answer true or false to the statements below: A 4. V D C Geometry 119

20 Unit 8 Practicing Proofs 1. Given: Parallelogram PQRS; S K R Prove: P J Q Statements Reasons 1. PQRS; Given: ; Prove: QRST is a parallelogram T 3 2 S Q 1 4 R Statements Reasons 1. ; QRST is a parallelogram. 6. (cont) Geometry 120

21 Unit 8 Practicing Proofs (cont) 3. Given: D y x C Prove: is a parallelogram. Statements A x y Reasons 1. ; is a parallelogram 5.. Geometry 121

22 Unit 8 Worksheet 4 1. Look at the coordinate grid below. Two points are to be added to the grid to form a square. a. Place two points in Quadrant 2 b. Place two points in Quadrant 3 that would form a square with that would form a square with the existing points. the existing points. Give the coordinates of the two points Give the coordinates of the two points. Complete the sketch of the square. Complete the sketch of the square. 2. Look at the coordinate grid below. Two points are to be added to the grid to form a rectangle with an area of 20 square units. a. Place two points in Quadrant 4 so b. Place two points in Quadrant 1 so that a rectangle with an area of that a rectangle with an area of 20 sq. units is formed. 20 sq. units is formed. Give the coordinates of the two points. Complete the sketch of the rectangle. Give the coordinates of the two points. Complete the sketch of the rectangle. 3. Look at the coordinate grid below. Point D is to be added in Quadrant 1to form a square. The slope of is and the slope of is. a. Use the slope information to help you plot point D to form a square. Complete the sketch of the square. Give the coordinates of point D. b. Use slopes to show that ACD has 4 right angles A c. Use the distance formula to show that all 4 sides in ACD are congruent. C (cont) Geometry 122

23 Unit 8 Worksheet 4 (cont) 4. The points (2, 1), (5, 1) and (2, 1) are plotted below. a. Plot a fourth point in quadrant 4 that will make a parallelogram. Give the coordinate of that point. Complete the sketch of the parallelogram. b. Plot a fourth point in quadrant 1 that will make a parallelogram. Give the coordinate of that point. Complete the sketch of the parallelogram. c. Plot a fourth point in quadrant 3 that will make a parallelogram. Give the coordinate of that point. Complete the sketch of the parallelogram. 5. The points ( 1, 1), ( 1, 3) and (1, 1) are plotted below. a. Plot a fourth point in quadrant 1 that will make a parallelogram. Give the coordinate of that point. Complete the sketch of the parallelogram. b. Plot a fourth point in quadrant 2 that will make a parallelogram. Give the coordinate of that point. Complete the sketch of the parallelogram. c. Plot a fourth point in quadrant 4 that will make a parallelogram. Give the coordinate of that point. Complete the sketch of the parallelogram. Geometry 123

24 Unit 8 Review In problems 1 22, choose the correct multiple choice response. NOTE: Diagrams are not drawn to scale. 1. What is the value of x? A C. 150 D. 120 x 2. Determine the value of x. A C. 9 D (8x + 1) 95 (5x 4) Determine the sum of the exterior angles of an octagon. A C. 360 D Determine the measure of each interior angle of a regular sided polygon with 9 sides. A C D Determine the measure of each exterior angle of a regular polygon with 12 sides. A C. 216 D The measure of an interior angle of a regular polygon is 162. How many sides does the polygon have? A. 18 sides. 20 sides C. 16 sides D. 10 sides 7. Determine the value of x? A C. 60 D (cont) Geometry x

25 Unit 8 Review (cont) 8. If the sum of the interior angles of a polygon equals 3780, how many sides does the polygon have? A C. 20 D What is the measure of each interior angle of a regular hexagon? A C. 45 D What are the values of the variables in the given parallelogram? A. x = 7, y = 9. x = 7, y = 65 C. x = 5, y = 71 D. x = 3, y = If FH = 30, find FK. A C. 15 D PQVT is a rhombus. Determine the value of x. A C. 70 D. 35 T 13. If PQRS is a rhombus, which statement must be true? A. is a right angle. C. P D. F J 12 K (6x 8) G H P (2y + 16) 110 x V S (4x + 6) Q Q R 14. Which statement is true? A. All quadrilaterals are rectangles. All rectangles are quadrilaterals C. All rectangles are squares D. All quadrilaterals are squares (cont) Geometry 125

26 Unit 8 Review (cont) 15. Determine the value of x. A C. 12 D. 8 2y 10 x + 6 3x 6 y In the diagram 1 = 9x, 2 = x + y Determine the values of x and y A. x = 20, y = 165. x = 10, y = 80 C. x = 20, y = 160 D. x = 10, y = and are congruent base angles of isosceles trapezoid JKLM. If = (18x + 5), = (14x + 15) and = (17x + 10), determine the value of x. A.. 2 C. 15 D The perimeter of square MNOP is 72 inches, and NO = 2x + 6. What is the value of x? A C. 6 D Determine the length of in the trapezoid shown. A C. 13 D Which quadrilateral has two pairs of consecutive congruent sides, but opposite sides are not congruent? A. Kite. Rhombus C. Trapezoid D. Parallelogram (cont) N H K 4x + 1 5x L I M Geometry 126

27 Unit 8 Review (cont) 21. What is the most specific name for the figure shown? A. Quadrilateral. Parallelogram C. Trapezoid D. Rectangle 22. Determine the value of x in the given parallelogram. A C. 4 D x + y 4x + 3y Work the following, showing all work. 2x + 7y 23. Determine the values of x and y x + y 24. ACD is an isosceles trapezoid with midsegment. Determine the following: 10 (3x + 2) C n = EF = E 3n 4 F x = = A (2x 17) 36 D 25. ACD is a parallelogram. Determine the following. x = 3x + 2y C y = 7x y z 2 E z z = AC = A 26 D (cont) Geometry 127

28 Unit 8 Review (cont) 26. ACD is a rectangle with perimeter 96 meters. Determine the following. A = 28 E 2n + 8 = n = D 6n Given a 25-gon: a. What is the sum of the measures of the interior angles? b. What is the sum of the measures of the exterior angles? C C = 28. Sketch LMNP if L (2, 1), M (1, 4), N (7, 6), and P (8, 3). Prove that LMNP is a rectangle. 29. The points (1, 1), (4, 1) and (1, 4) are plotted below. A. Plot a fourth point in. Plot a fourth point in C. Plot a fourth point in quadrant 4 that will make quadrant 3 that will make quadrant 1 that will a parallelogram. a parallelogram. make a parallelogram. Geometry 128

29 Unit 8 Systems Practice What values must x and y have to make each quadrilateral a parallelogram? (8x 6) o 3y o y 2 x 42 o (3x 40) ( y + 30) (7y 2) o 26 3x 2y (4x + 1) o 4x + y 9y o 3x o Geometry 129

30 (5n + 1) Unit 8 Quadrilateral & Polygon Worksheet [1-12]: Solve for the variables. Give the best name for each of the following based upon given information and calculations. Show logical & appropriate work! {Names of Quadrilaterals are: Quadrilateral, Parallelogram, Rectangle, Rhombus, Square, Trapezoid, & Isosceles Trapezoid} x = 5x o 4y o y = 70 o Name: 2. x = y = Name 3. x = y = Name: 4. x = y = Name: 52 o x o x o y o y o 37 o (8n 11) 5. x = y = n = Name: 6. x = 8x Name Perimeter of quadrilateral is 90 cm 24 o 5n + 7 (7x 19) o y o (5x + 3) o 3n + 2 3x +1 A 115 o (12x 19) o (cont) y o 4n + 12 x o 2n + 40 Perimeter of quadrilateral is 274 meters. (x 4) feet C 15 feet 24 feet D 7. x = y = n = Name 8. x = C = Name Geometry 130

31 Unit 8 Quadrilateral & Polygon Worksheet (cont) x = 3x + 5 C 2x 2 C AD = A 46 5x 1 D 2x + 1 (4a + 1) o 3x 3 (6a 13) o A Name = 10. x = z = Name x = Quadrilateral ACD is a parallelogram. Quadrilateral ACD is a rhombus. 24 C 63 o 17 x o (2y + 1) o 7n + 3 y = m = n = 12. x = y = A D A D z = 5m 6 = 13. Find the sum of the measures of the interior angles for the following convex polygons. a. 17-gon b. 34-gon c. 51-gon 13.a. 14. Find the measure of each exterior angle for the following regular polygons. b. c. a. Pentagon b. Heptagon c. 45-gon 14.a. b. c. 15. Find the measure of each interior angle for the following regular polygons. 15.a. a. Decagon b. Octagon c. 21-gon b. c. 16. Find the number of sides for a convex polygon whose interior angle sum is: 16a. a o b o c o b. 17. Find the number of sides for the following regular polygons, given: y o 25 o c. a. The measure of each exterior angle is 7.5 o. 17.a. b. The measure of each interior angles is b. x o z o D C Geometry 131

32 Quadrilateral Tree Quadrilateral Kite Trapezoid Parallelogram Isosceles Trapezoid Rectangle Rhombus Please note: Midsegment = average of the bases ase # Square midsegment 1. ase # 1 or Geometry 132

33 Unit 8 Extra Practice In problems 1-3 find the requested parts. (Remember names of Quadrilaterals are: Quadrilateral, Parallelogram, Rectangle, Rhombus, Square, Trapezoid, Isosceles Trapezoid, & Kite} 1. Perimeter = 144 meters x = x o y o 52 o 3n +13 y = n = est Name: 2. 8n 7. 2n 4 C x = = 2n + 5 n = = A (5x + 3) o 4n + 5 (3x + 35) o D est Name: 3. y o (10n 13) x = = x o n = (7n + 5) 65 o = est Name: 4. Find the measure of each interior angle for a regular 15-gon. 5. Find the measure of each exterior angle for a regular heptagon. 6. Find the number of sides for a regular polygon with each exterior angle measuring 15 o. 7. Find the number of sides for a regular polygon with each interior angle measuring 172 o. Geometry 133

34 Properties of Quadrilaterals Property Parallelogram Rectangle Rhombus Square Trapezoid Kite Two pairs of opposite sides are parallel. Has exactly one pair of parallel sides. Two pairs of opposite sides are congruent. Has two pairs of consecutive congruent sides, but opposite sides are not congruent. All sides are congruent. Diagonals are congruent. Diagonals are perpendicular. A diagonal bisects two angles. A diagonal forms two congruent triangles. Diagonals bisect each other. Opposite angles are congruent. All angles are right angles. Consecutive interior angles are supplementary. Geometry 134

35 Unit 10 Objective 0 1. A rhombus has a diagonal that lies on the line y = x + 1. What is the slope of the other diagonal of the rhombus? 2. Find the measure of in parallelogram ACD. Z A LMNP is a rectangle. 2 and 3 are congruent. What is the measure of 1? L 1 D M C 50 P In the diagram shown the measure of 1 is 4 times as large as the measure of 2. What is the measure of 2? N Which multiple choice serves as a counterexample to the statement: All quadrilaterals have four right angles. A. A square. A rhombus C. A rectangle 6. In rectangle ACD, A =, CD =. determine the value of x. 7. PQRS is a rhombus. What is the value of y? x + 5 P (cont) S y 6 2x Q Geometry 135 S

36 Unit 10 Objective 0 (cont) 8. Currently the only way to travel from the city of Rio to the city of Phillie is by traveling through the city of Duke as shown in the drawing at the right. Engineers are thinking about building a road directly from the city of Rio to the city of Phillie as shown below. a. Determine the number of miles that the direct route frm Rio to Phillie would be. b. Determine how many miles would be saved by a person driving the direct route as compared to a person driving the long way through Duke. New Proposed Route Phillie 12 miles Phillie 12 miles Duke 5 miles Original Route Rio Duke 5 miles Rio 9. Given the parallelogram below, find the coordinates for P, without using any new variables. y (a, b) P (c, 0) x 10. For the quadrilateral shown, find W V 112 Y Z 47 Geometry 136

37 Geometry Unit Parts of a circle, including tangent lines. (Section 10.1) 2. Central angles and finding arc measures. (Section 10.2) 3. Apply properties of chords. (Section 10.3) 4. Use inscribed angles and inscribed polygons. (Section 10.4) 5. Interior and exterior angle relationships with circles. (Section 10.5) 6. Find segment lengths in circles. (Section 10.6) 7. Write and graph equations of circles. (Section 10.7) Review Unit 10 Worksheet 4 asic Terms & Tangents In problems 1 6 refer to O. Name each of the following: 1. Two radii and 2. A diameter 3. A secant 4. A tangent 5. Two chords and 6. A point of tangency In problems 7 11 refer to with radius P. Find the following: 7. If P = 4, then SP = 8. If SP = 16n, then P = 9. If is tangent to, then =. 10. If and are tangent to, then. 11. If is tangent to, then would be to. (cont) Geometry 137

38 Unit 10 Worksheet 4 asic Terms & Tangents (cont) In problems refer to O. 12. If = 60, then A = 13. If = 90, then C = 14. Name an inscribed polygon in the figure In problems 15 17, O and P are the centers of the circles. In problem 16, and are tangent to both circles and divides into segments whose lengths are shown OP = RS = HI = In the diagram for Problems 18 20, is tangent to O. 18. If DE = 12 and DO = 9, then OE = 19. If = 60 and OD = 9, then OE = 20. If DO = 5 and CE = 8, then DE = Geometry 138

39 Unit 10 Worksheet 5A In problems 1 4, and are chords. 1. If = 85 and = 73, then 1 =. 2. If = 136 and = 96, then 1 =. 3. If 1 = 54 and = 78, then =. 4. If 1 = 48 and = 42, then =. In problems 5 7, and are tangents. 5. If = 280, then =. 6. If = 96, then =. 7. If = 90, then =. In problems 8 10, is a tangent. 8. If = 120 and = 40, then =. 9. If = 45 and = 55, then =. 10. If = 50 and = 110, then =. In problems 11 15, and are secants. 11. If = 100 and = 20, then =. 12. If = 130 and = 40, then =. 13. If = 25 and = 25, then =. 14. If = 40 and = 130, then =. 15. If = 90, = 60, and = 80, then =. In problems 16 19, is tangent to the circle at point E. 16. If = 100 and = 20, then =. 17. If = 25 and = 25, then =. 18. If = 95 and = 25, then =. 19. If = 40 and = 138, then =. Geometry 139

40 In problems 1 6, find the values of a, b, and c. Unit 10 Worksheet a = b = c = a = b = c = a = b = c = a = b = c = a = b = c = a = b = c = is a diameter of O. is tangent to O at A. = 80, = 20, and = = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 9 = 10 = Geometry 140

41 Unit 10 Worksheet 6A Solve for x. Show your work x (cont) Geometry 141

42 Unit 10 Worksheet 6A (cont) A = 48 Find the radius. Given: Circle O = 124, = 140, = 62. Find the measure of 1 through 10 Geometry 142

43 Unit 10 Worksheet 6 In O, = 50 and = 70. Find each of the following: In O, = 60, = 80 = 110, is tangent to O at C, and = 130. Find each of the following: O has arc measures as shown. and are tangent at J and M, respectively. Find the following: (cont) Geometry 143

44 Unit 10 Worksheet is tangent to O at Q. If = 15 and PO = 17, find the radius of the circle. 18. Find the total number of common tangents that can be drawn to two coplanar circles that are externally tangent. 19. Complete: If a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the line is. In O, 1 2 and 3 = 100. Find the following: In P, = 300. Find the following: AD = 27. D = X PQ = 16; OX = 6 ; OX = 5 OY = 7; RS = GH = 24; OG = 30. Find the length of a chord that is 3 cm from the center of a circle with radius 9 cm. Geometry 144

45 Unit 10 Worksheet 7 Solve for x. Show all work (cont) Geometry 145

46 Unit 10 Worksheet x 2 + (y 4) 2 = Center = (5, 1), radius = Center = Write the equation for the circle Radius = given the above information. Geometry 146

47 Unit 10 Review In problems 1 17 select the correct multiple choice response 1. EF and EG are tangents to the circle shown. Find the measure of. A C. 60 D Find the value of x. A C. 22 D HJ is tangent to P. Find the value of x. A C. 25 D Find in P A C. 288 D Find. A C. 152 D In P the 42. Find A C. 96 D WY is tangent to the circle shown. = 74. Find. A C. 212 D Find the value of x in the circle shown. A C. 49 D Find the value of x. A C. 60 D Find the value of x in the circle shown. A C. 88 D. 46 Geometry 147

48 11. What is the length of? 266 A C. 12 D Find A C. 64 D Find CD. A C. 9 D. 18 Solve the following problems. Show all work. 18. C and AC are tangents to the given circle. Find the value of x. 13. In the circle shown, UP = 2, NP = 4, and UW = 18. Find LP. A C. 12 D If = 110, find 14. Find in O. A C. 156 D In Q = 220 a. Find b. Find 15. State the radius of the circle whose equation is (x 1) 2 + (y 3) 2 = 4 A C. 8 D Find the value of x. 16. State the center of the radius of the circle whose equation is (x + 6) 2 + (y 7) 2 = 1 A. (6, 7). (6, 7) C. ( 6, 7) D. ( 6, 7) 22. Circle O is inscribed in quadrilateral ACD. A = 12 and CD = Find the perimeter of quadrilateral ACD. 6 C D Geometry 148 A

49 Problems 1-4 refer to Unit 10 Worksheet Arc, Central Angles, and Chords O. Find the measure of each arc. 1. = 2. = 3. = 4. = Find the value of x. Each angle shown is a central angle x = x = x = 8. At 10 o clock the hands of a clock form an angle of. 9. At seven o clock the hands of a clock form an angle of. 10. If the hands of a clock form an angle of 30, the time is o clock. In problems 11 16, is a diameter of O. 11. E = 12. O = 13. = 14. = 15. = 16. DE = Complete the following: 17. A = 8, CD = 9 ED = 18. HI = 19. WY = 20. CD = Geometry 149

50 Unit 10 Circles & Special Right Triangles 1. Find A 2. Find A 3. is tangent to A C C Find A 5 A A 4. Find the value of x, y, and 5. OT = 9, RS = 18, 6. = 90 and XZ = 13 Find OR Find XY 7. Find JK 8. Find LM and LO 9. Find 10. Find 11. Find K and 12. Find SU and Geometry 150

Postulates, Theorems, and Corollaries. Chapter 1

Postulates, Theorems, and Corollaries. Chapter 1 Chapter 1 Post. 1-1-1 Through any two points there is exactly one line. Post. 1-1-2 Through any three noncollinear points there is exactly one plane containing them. Post. 1-1-3 If two points lie in a

More information

Geometry. Released Test Questions. 2 In the diagram below,! 1 "!4. Consider the arguments below.

Geometry. Released Test Questions. 2 In the diagram below,! 1 !4. Consider the arguments below. 1 Which of the following best describes deductive reasoning? using logic to draw conclusions based on accepted statements accepting the meaning of a term without definition defining mathematical terms

More information

1. AREAS. Geometry 199. A. Rectangle = base altitude = bh. B. Parallelogram = base altitude = bh. C. Rhombus = 1 product of the diagonals = 1 dd

1. AREAS. Geometry 199. A. Rectangle = base altitude = bh. B. Parallelogram = base altitude = bh. C. Rhombus = 1 product of the diagonals = 1 dd Geometry 199 1. AREAS A. Rectangle = base altitude = bh Area = 40 B. Parallelogram = base altitude = bh Area = 40 Notice that the altitude is different from the side. It is always shorter than the second

More information

6.1: Date: Geometry. Polygon Number of Triangles Sum of Interior Angles

6.1: Date: Geometry. Polygon Number of Triangles Sum of Interior Angles 6.1: Date: Geometry Polygon Number of Triangles Sum of Interior Angles Triangle: # of sides: # of triangles: Quadrilateral: # of sides: # of triangles: Pentagon: # of sides: # of triangles: Hexagon: #

More information

Name: Second semester Exam Honors geometry Agan and Mohyuddin. May 13, 2014

Name: Second semester Exam Honors geometry Agan and Mohyuddin. May 13, 2014 Name: Second semester Exam Honors geometry Agan and Mohyuddin May 13, 2014 1. A circular pizza has a diameter of 14 inches and is cut into 8 equal slices. To the nearest tenth of a square inch, which answer

More information

U4 Polygon Notes January 11, 2017 Unit 4: Polygons

U4 Polygon Notes January 11, 2017 Unit 4: Polygons Unit 4: Polygons 180 Complimentary Opposite exterior Practice Makes Perfect! Example: Example: Practice Makes Perfect! Def: Midsegment of a triangle - a segment that connects the midpoints of two sides

More information

Geometry. Geometry is one of the most important topics of Quantitative Aptitude section.

Geometry. Geometry is one of the most important topics of Quantitative Aptitude section. Geometry Geometry is one of the most important topics of Quantitative Aptitude section. Lines and Angles Sum of the angles in a straight line is 180 Vertically opposite angles are always equal. If any

More information

Section Congruence Through Constructions

Section Congruence Through Constructions Section 10.1 - Congruence Through Constructions Definitions: Similar ( ) objects have the same shape but not necessarily the same size. Congruent ( =) objects have the same size as well as the same shape.

More information

Geometry Practice. 1. Angles located next to one another sharing a common side are called angles.

Geometry Practice. 1. Angles located next to one another sharing a common side are called angles. Geometry Practice Name 1. Angles located next to one another sharing a common side are called angles. 2. Planes that meet to form right angles are called planes. 3. Lines that cross are called lines. 4.

More information

Geometry SIA #2. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Geometry SIA #2. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. Class: Date: Geometry SIA #2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the value of x. a. 4 b. 8 c. 6.6 d. 6 2. Find the length of the midsegment.

More information

Geometry/Trigonometry Unit 5: Polygon Notes Period:

Geometry/Trigonometry Unit 5: Polygon Notes Period: Geometry/Trigonometry Unit 5: Polygon Notes Name: Date: Period: # (1) Page 270 271 #8 14 Even, #15 20, #27-32 (2) Page 276 1 10, #11 25 Odd (3) Page 276 277 #12 30 Even (4) Page 283 #1-14 All (5) Page

More information

Geometry Quarter 4 Test Study Guide

Geometry Quarter 4 Test Study Guide Geometry Quarter 4 Test Study Guide 1. Write the if-then form, the converse, the inverse and the contrapositive for the given statement: All right angles are congruent. 2. Find the measures of angles A,

More information

Chapter 2 Diagnostic Test

Chapter 2 Diagnostic Test Chapter Diagnostic Test STUDENT BOOK PAGES 68 7. Calculate each unknown side length. Round to two decimal places, if necessary. a) b). Solve each equation. Round to one decimal place, if necessary. a)

More information

Second Semester Exam Review Packet

Second Semester Exam Review Packet Geometry Name Second Semester Exam Review Packet CHAPTER 7 THE PYTHAGOREAN THEOREM. This theorem is used to find the lengths of the sides of a right triangle. Label the parts of the right triangle. What

More information

Geometry Third Quarter Study Guide

Geometry Third Quarter Study Guide Geometry Third Quarter Study Guide 1. Write the if-then form, the converse, the inverse and the contrapositive for the given statement: All right angles are congruent. 2. Find the measures of angles A,

More information

Modeling with Geometry

Modeling with Geometry Modeling with Geometry 6.3 Parallelograms https://mathbitsnotebook.com/geometry/quadrilaterals/qdparallelograms.html Properties of Parallelograms Sides A parallelogram is a quadrilateral with both pairs

More information

Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets

Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets Using coordinates, I can find the intersection of the medians of a triangle that meet at a point that is two-thirds of the way along each median

More information

Thomas Jefferson High School for Science and Technology Program of Studies TJ Math 1

Thomas Jefferson High School for Science and Technology Program of Studies TJ Math 1 Course Description: This course is designed for students who have successfully completed the standards for Honors Algebra I. Students will study geometric topics in depth, with a focus on building critical

More information

Period: Date Lesson 13: Analytic Proofs of Theorems Previously Proved by Synthetic Means

Period: Date Lesson 13: Analytic Proofs of Theorems Previously Proved by Synthetic Means : Analytic Proofs of Theorems Previously Proved by Synthetic Means Learning Targets Using coordinates, I can find the intersection of the medians of a triangle that meet at a point that is two-thirds of

More information

B = the maximum number of unique scalene triangles having all sides of integral lengths and perimeter less than 13

B = the maximum number of unique scalene triangles having all sides of integral lengths and perimeter less than 13 GEOMETRY TEAM #1 A = the m C in parallelogram ABCD with m B= (4x+ 15), m D= (6x+ ) B = the degree measure of the smallest angle in triangle ABC with m A= ( x+ 0), m B= ( x+ 7), m C= (x 15) Find the value

More information

15. K is the midpoint of segment JL, JL = 4x - 2, and JK = 7. Find x, the length of KL, and JL. 8. two lines that do not intersect

15. K is the midpoint of segment JL, JL = 4x - 2, and JK = 7. Find x, the length of KL, and JL. 8. two lines that do not intersect Name: Period Date Pre-AP Geometry Fall Semester Exam REVIEW *Chapter 1.1 Points Lines Planes Use the figure to name each of the following: 1. three non-collinear points 2. one line in three different ways

More information

STANDARDS OF LEARNING CONTENT REVIEW NOTES GEOMETRY. 3 rd Nine Weeks,

STANDARDS OF LEARNING CONTENT REVIEW NOTES GEOMETRY. 3 rd Nine Weeks, STANDARDS OF LEARNING CONTENT REVIEW NOTES GEOMETRY 3 rd Nine Weeks, 2016-2017 1 OVERVIEW Geometry Content Review Notes are designed by the High School Mathematics Steering Committee as a resource for

More information

fall08ge Geometry Regents Exam Test Sampler fall08 4 The diagram below shows the construction of the perpendicular bisector of AB.

fall08ge Geometry Regents Exam Test Sampler fall08  4 The diagram below shows the construction of the perpendicular bisector of AB. fall08ge 1 Isosceles trapezoid ABCD has diagonals AC and BD. If AC = 5x + 13 and BD = 11x 5, what is the value of x? 1) 8 4 The diagram below shows the construction of the perpendicular bisector of AB.

More information

Unit Lesson Plan: Measuring Length and Area: Area of shapes

Unit Lesson Plan: Measuring Length and Area: Area of shapes Unit Lesson Plan: Measuring Length and Area: Area of shapes Day 1: Area of Square, Rectangles, and Parallelograms Day 2: Area of Triangles Trapezoids, Rhombuses, and Kites Day 3: Quiz over Area of those

More information

Section 1-1 Points, Lines, and Planes

Section 1-1 Points, Lines, and Planes Section 1-1 Points, Lines, and Planes I CAN. Identify and model points, lines, and planes. Identify collinear and coplanar points and intersecting lines and planes in space. Undefined Term- Words, usually

More information

Unit 3: Triangles and Polygons

Unit 3: Triangles and Polygons Unit 3: Triangles and Polygons Background for Standard G.CO.9: Prove theorems about triangles. Objective: By the end of class, I should Example 1: Trapezoid on the coordinate plane below has the following

More information

Geometry: A Complete Course

Geometry: A Complete Course Geometry: omplete ourse with Trigonometry) Module Progress Tests Written by: Larry. ollins Geometry: omplete ourse with Trigonometry) Module - Progress Tests opyright 2014 by VideotextInteractive Send

More information

GEOMETRY PRACTICE TEST END OF COURSE version A (MIXED) 2. Which construction represents the center of a circle that is inscribed in a triangle?

GEOMETRY PRACTICE TEST END OF COURSE version A (MIXED) 2. Which construction represents the center of a circle that is inscribed in a triangle? GEOMETRY PRACTICE TEST END OF COURSE version A (MIXED) 1. The angles of a triangle are in the ratio 1:3:5. What is the measure, in degrees, of the largest angle? A. 20 B. 30 C. 60 D. 100 3. ABC and XYZ

More information

10.6 Area and Perimeter of Regular Polygons

10.6 Area and Perimeter of Regular Polygons 10.6. Area and Perimeter of Regular Polygons www.ck12.org 10.6 Area and Perimeter of Regular Polygons Learning Objectives Calculate the area and perimeter of a regular polygon. Review Queue 1. What is

More information

Assignment List. Chapter 1 Essentials of Geometry. Chapter 2 Reasoning and Proof. Chapter 3 Parallel and Perpendicular Lines

Assignment List. Chapter 1 Essentials of Geometry. Chapter 2 Reasoning and Proof. Chapter 3 Parallel and Perpendicular Lines Geometry Assignment List Chapter 1 Essentials of Geometry 1.1 Identify Points, Lines, and Planes 5 #1, 4-38 even, 44-58 even 27 1.2 Use Segments and Congruence 12 #4-36 even, 37-45 all 26 1.3 Use Midpoint

More information

If two sides and the included angle of one triangle are congruent to two sides and the included angle of 4 Congruence

If two sides and the included angle of one triangle are congruent to two sides and the included angle of 4 Congruence Postulates Through any two points there is exactly one line. Through any three noncollinear points there is exactly one plane containing them. If two points lie in a plane, then the line containing those

More information

1 William is drawing pictures of cross sections of the right circular cone below.

1 William is drawing pictures of cross sections of the right circular cone below. 1 William is drawing pictures of cross sections of the right circular cone below. Which drawing can not be a cross section of a cone? 1) 2) 3) 4) 2 An equation of a line perpendicular to the line represented

More information

5B.4 ~ Calculating Sine, Cosine, Tangent, Cosecant, Secant and Cotangent WB: Pgs :1-10 Pgs : 1-7

5B.4 ~ Calculating Sine, Cosine, Tangent, Cosecant, Secant and Cotangent WB: Pgs :1-10 Pgs : 1-7 SECONDARY 2 HONORS ~ UNIT 5B (Similarity, Right Triangle Trigonometry, and Proof) Assignments from your Student Workbook are labeled WB Those from your hardbound Student Resource Book are labeled RB. Do

More information

Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.

Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry. Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know

More information

Geometry SIA #2 Practice Exam

Geometry SIA #2 Practice Exam Class: Date: Geometry SIA #2 Practice Exam Short Answer 1. Justify the last two steps of the proof. Given: RS UT and RT US Prove: RST UTS Proof: 1. RS UT 1. Given 2. RT US 2. Given 3. ST TS 3.? 4. RST

More information

NAEP Released Items Aligned to the Iowa Core: Geometry

NAEP Released Items Aligned to the Iowa Core: Geometry NAEP Released Items Aligned to the Iowa Core: Geometry Congruence G-CO Experiment with transformations in the plane 1. Know precise definitions of angle, circle, perpendicular line, parallel line, and

More information

Geometry/Pre AP Geometry Common Core Standards

Geometry/Pre AP Geometry Common Core Standards 1st Nine Weeks Transformations Transformations *Rotations *Dilation (of figures and lines) *Translation *Flip G.CO.1 Experiment with transformations in the plane. Know precise definitions of angle, circle,

More information

GEOMETRY Spring Packet. Good Luck To: Date:

GEOMETRY Spring Packet. Good Luck To: Date: Good Luck To: Date: MA.912.G.1.1 1. has an endpoint at (2, 1) and a midpoint at (8, 3). Which measure is closest to the length of? A. 20.4 units B. 8.9 units C. 14.4 units D. 11.7 units MA.912.G.5.4 2.

More information

8.1 Find Angle Measures in Polygons

8.1 Find Angle Measures in Polygons VOCABULARY 8.1 Find Angle Measures in Polygons DIAGONAL Review: EQUILATERAL EQUIANGULAR REGULAR CLASSIFYING POLYGONS Polygon Interior Angle Theorem: The sum of the measures of the interior angles of a

More information

Points, lines, angles

Points, lines, angles Points, lines, angles Point Line Line segment Parallel Lines Perpendicular lines Vertex Angle Full Turn An exact location. A point does not have any parts. A straight length that extends infinitely in

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Name ate hapter 7 Maintaining Mathematical Proficiency Solve the equation by interpreting the expression in parentheses as a single quantity. 1. 5( 10 x) = 100 2. 6( x + 8) 12 = 48 3. ( x) ( x) 32 + 42

More information

Carnegie Learning High School Math Series: Geometry Indiana Standards Worktext Correlations

Carnegie Learning High School Math Series: Geometry Indiana Standards Worktext Correlations Carnegie Learning High School Math Series: Logic and Proofs G.LP.1 Understand and describe the structure of and relationships within an axiomatic system (undefined terms, definitions, axioms and postulates,

More information

Chapter 11 Areas of Polygons and Circles

Chapter 11 Areas of Polygons and Circles Section 11-1: Areas of Parallelograms and Triangles SOL: G.14 The student will use similar geometric objects in two- or three-dimensions to a) compare ratios between side lengths, perimeters, areas, and

More information

Definition / Postulates / Theorems Checklist

Definition / Postulates / Theorems Checklist 3 undefined terms: point, line, plane Definition / Postulates / Theorems Checklist Section Definition Postulate Theorem 1.2 Space Collinear Non-collinear Coplanar Non-coplanar Intersection 1.3 Segment

More information

Polygons, Congruence, Similarity Long-Term Memory Review Grade 8 Review 1

Polygons, Congruence, Similarity Long-Term Memory Review Grade 8 Review 1 Review 1 1. In the diagram below, XYZ is congruent to CDE XYZ CDE. Y D E X Z C Complete the following statements: a) C b) XZ c) CDE d) YZ e) Z f) DC 2. In the diagram below, ABC is similar to DEF ABC DEF.

More information

Houghton Mifflin Harcourt Geometry 2015 correlated to the New York Common Core Learning Standards for Mathematics Geometry

Houghton Mifflin Harcourt Geometry 2015 correlated to the New York Common Core Learning Standards for Mathematics Geometry Houghton Mifflin Harcourt Geometry 2015 correlated to the New York Common Core Learning Standards for Mathematics Geometry Standards for Mathematical Practice SMP.1 Make sense of problems and persevere

More information

COURSE OBJECTIVES LIST: GEOMETRY

COURSE OBJECTIVES LIST: GEOMETRY COURSE OBJECTIVES LIST: GEOMETRY Geometry Honors is offered. PREREQUISITES: All skills from Algebra I are assumed. A prerequisites test is given during the first week of class to assess knowledge of these

More information

Contents. Lines, angles and polygons: Parallel lines and angles. Triangles. Quadrilaterals. Angles in polygons. Congruence.

Contents. Lines, angles and polygons: Parallel lines and angles. Triangles. Quadrilaterals. Angles in polygons. Congruence. Colegio Herma. Maths Bilingual Departament Isabel Martos Martínez. 2015 Contents Lines, angles and polygons: Parallel lines and angles Triangles Quadrilaterals Angles in polygons Congruence Similarity

More information

FALL SEMESTER EXAM Directions: You must show work for all the problems. Unit 1. Angle. Angle Addition Postulate. Angle Bisector. Length of a segment

FALL SEMESTER EXAM Directions: You must show work for all the problems. Unit 1. Angle. Angle Addition Postulate. Angle Bisector. Length of a segment Name FALL SEMESTER EXAM Directions: You must show work for all the problems. Unit 1 Period Angle Angle Addition Postulate Angle Bisector Length of a segment Line Midpoint Right Angle Segment Segment Addition

More information

Russell County Pacing Guide

Russell County Pacing Guide August Experiment with transformations in the plane. 1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance

More information

FLORIDA GEOMETRY EOC TOOLKIT

FLORIDA GEOMETRY EOC TOOLKIT FLORIDA GEOMETRY EOC TOOLKIT CORRELATION Correlated to the Geometry End-of-Course Benchmarks For more information, go to etacuisenaire.com\florida 78228IS ISBN 978-0-7406-9565-0 MA.912.D.6.2 Find the converse,

More information

Texas High School Geometry

Texas High School Geometry Texas High School Geometry This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet

More information

5.5 Right Triangles. 1. For an acute angle A in right triangle ABC, the trigonometric functions are as follow:

5.5 Right Triangles. 1. For an acute angle A in right triangle ABC, the trigonometric functions are as follow: 5.5 Right Triangles 1. For an acute angle A in right triangle ABC, the trigonometric functions are as follow: sin A = side opposite hypotenuse cos A = side adjacent hypotenuse B tan A = side opposite side

More information

10-2. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry

10-2. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Find the unknown side lengths in each special right triangle. 1. a 30-60 -90 triangle with hypotenuse 2 ft 2. a 45-45 -90 triangle with leg length

More information

Ref: GIS Math G 9 C.D

Ref: GIS Math G 9 C.D Ref: GIS Math G 9 C.D. 2015-2016 2011-2012 SUBJECT : Math TITLE OF COURSE : Geometry GRADE LEVEL : 9 DURATION : ONE YEAR NUMBER OF CREDITS : 1.25 Goals: Congruence G-CO Experiment with transformations

More information

MATH-G Geometry SOL Test 2015 Exam not valid for Paper Pencil Test Sessions

MATH-G Geometry SOL Test 2015 Exam not valid for Paper Pencil Test Sessions MATH-G Geometry SOL Test 2015 Exam not valid for Paper Pencil Test Sessions [Exam ID:2LKRLG 1 Which Venn diagram accurately represents the information in the following statement? If a triangle is equilateral,

More information

UNIT 6: Connecting Algebra & Geometry through Coordinates

UNIT 6: Connecting Algebra & Geometry through Coordinates TASK: Vocabulary UNIT 6: Connecting Algebra & Geometry through Coordinates Learning Target: I can identify, define and sketch all the vocabulary for UNIT 6. Materials Needed: 4 pieces of white computer

More information

Geometry Spring Final Review #1, 2014

Geometry Spring Final Review #1, 2014 Class: Date: Geometry Spring Final Review #1, 2014 Short Answer 1. Find the measure of each interior angle of a regular 45-gon. 2. Find the measure of each exterior angle of a regular decagon. 3. The door

More information

Geometry Semester 1 REVIEW Must show all work on the Review and Final Exam for full credit.

Geometry Semester 1 REVIEW Must show all work on the Review and Final Exam for full credit. Geometry Semester 1 REVIEW Must show all work on the Review and Final Exam for full credit. NAME UNIT 1: 1.6 Midpoint and Distance in the Coordinate Plane 1. What are the coordinates of the midpoint of

More information

Geometry H Semester 2 Practice Exam

Geometry H Semester 2 Practice Exam 1. tire has a radius of 15 inches. What is the approximate circumference, in inches, of the tire?. 47 in.. 94 in.. 188 in. D. 707 in. 2. In the figure below, adjacent sides of the polygon are perpendicular.

More information

Maryland Geometry UNIT 1: FOUNDATIONS OF GEOMETRY. Core

Maryland Geometry UNIT 1: FOUNDATIONS OF GEOMETRY. Core Core Geometry builds upon students' command of geometric relationships and formulating mathematical arguments. Students learn through discovery and application, developing the skills they need to break

More information

MATHia Unit MATHia Workspace Overview TEKS

MATHia Unit MATHia Workspace Overview TEKS 1 Tools of Geometry Lines, Rays, Segments, and Angles Distances on the Coordinate Plane Parallel and Perpendicular Lines Angle Properties Naming Lines, Rays, Segments, and Angles Working with Measures

More information

Reteaching Transversals and Angle Relationships

Reteaching Transversals and Angle Relationships Name Date Class Transversals and Angle Relationships INV Transversals A transversal is a line that intersects two or more coplanar lines at different points. Line a is the transversal in the picture to

More information

1997 Geometry part 1

1997 Geometry part 1 1997 Geometry part 1 1. In the figure below is similar to E, is the midpoint of segment and the perimeter of E = 10. Find the perimeter of. a) 15 b) 0 c) 5 d) 30 e) 40 E. In the figure below m 1 = m and

More information

Level 1 Geometry Review Topics

Level 1 Geometry Review Topics Level 1 Geometry Review Topics Logic If-then, inverse, converse, and contrapositive Complementary and Supplementary Angles Vertical Angles Congruent Triangles ASA, SAS, SSS, AAS, HL, CPCTC Altitudes, Medians,

More information

Be sure to label all answers and leave answers in exact simplified form.

Be sure to label all answers and leave answers in exact simplified form. Pythagorean Theorem word problems Solve each of the following. Please draw a picture and use the Pythagorean Theorem to solve. Be sure to label all answers and leave answers in exact simplified form. 1.

More information

Shortcuts, Formulas & Tips

Shortcuts, Formulas & Tips & present Shortcuts, Formulas & Tips For MBA, Banking, Civil Services & Other Entrance Examinations Vol. 3: Geometry Lines and Angles Sum of the angles in a straight line is 180 Vertically opposite angles

More information

3 Identify shapes as two-dimensional (lying in a plane, flat ) or three-dimensional ( solid ).

3 Identify shapes as two-dimensional (lying in a plane, flat ) or three-dimensional ( solid ). Geometry Kindergarten Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). 1 Describe objects in the environment using names of shapes,

More information

0617geo. Geometry CCSS Regents Exam PQR?

0617geo. Geometry CCSS Regents Exam PQR? 0617geo 1 In the diagram below, ABC DEF. 2 On the set of axes below, the vertices of PQR have coordinates P( 6,7), Q(2,1), and R( 1, 3). Which sequence of transformations maps ABC onto DEF? 1) a reflection

More information

1) AB CD 2) AB = CD 3) AE = EB 4) CE = DE

1) AB CD 2) AB = CD 3) AE = EB 4) CE = DE 1 In trapezoid RSTV with bases RS and VT, diagonals RT and SV intersect at Q. If trapezoid RSTV is not isosceles, which triangle is equal in area to RSV? 1) RQV 2) RST 3) RVT 4) SVT 2 In the diagram below,

More information

, y 2. ), then PQ = - y 1 ) 2. x 1 + x 2

, y 2. ), then PQ = - y 1 ) 2. x 1 + x 2 Tools of Geometry Chapter 1 Undefined Terms (p. 5) A point is a location. It has neither shape nor size. A line is made up of points and has no thickness or width. A plane is a flat surface made up of

More information

Geometry Semester Exam Review

Geometry Semester Exam Review Name: Hr: Geometry Semester Exam Review GET ORGANIZED. Successful studying begins with being organized. Bring this packet with you to class every day. DO NOT FALL BEHIND. Do the problems that are assigned

More information

0815geo. Geometry CCSS Regents Exam In the diagram below, a square is graphed in the coordinate plane.

0815geo. Geometry CCSS Regents Exam In the diagram below, a square is graphed in the coordinate plane. 0815geo 1 A parallelogram must be a rectangle when its 1) diagonals are perpendicular ) diagonals are congruent ) opposite sides are parallel 4) opposite sides are congruent If A' B' C' is the image of

More information

Geometry Skills. Topic Outline. Course Description and Philosophy

Geometry Skills. Topic Outline. Course Description and Philosophy Geometry Skills Topic Outline Course Description and Philosophy Geometry Skills is the second course in the 3-year skills sequence, following Algebra Skills, and preceding Algebra II Skills. This course

More information

Honors Geometry Semester Exam Review

Honors Geometry Semester Exam Review Name: Hr: Honors Geometry Semester Exam Review GET ORGANIZED. Successful studying begins with being organized. Bring this packet with you to class every day. DO NOT FALL BEHIND. Do the problems that are

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Name Date Chapter 1 Maintaining Mathematical Proficiency Simplify the expression. 1. 3 + ( 1) = 2. 10 11 = 3. 6 + 8 = 4. 9 ( 1) = 5. 12 ( 8) = 6. 15 7 = + = 8. 5 ( 15) 7. 12 3 + = 9. 1 12 = Find the area

More information

0117geo. Geometry CCSS Regents Exam y = 1 2 x + 8? 2 AB AC 3) 2AB + 2AC 4) AB + AC

0117geo. Geometry CCSS Regents Exam y = 1 2 x + 8? 2 AB AC 3) 2AB + 2AC 4) AB + AC 0117geo 1 Which equation represents the line that passes through the point ( 2,2) and is parallel to y = 1 2 x + 8? 1) y = 1 2 x 2) y = 2x ) y = 1 2 x + 4) y = 2x + Given ABC DEF, which statement is not

More information

Ch 1 Note Sheet L2 Key.doc 1.1 Building Blocks of Geometry

Ch 1 Note Sheet L2 Key.doc 1.1 Building Blocks of Geometry 1.1 uilding locks of Geometry Read page 28. It s all about vocabulary and notation! To name something, trace the figure as you say the name, if you trace the figure you were trying to describe you re correct!

More information

B. Algebraic Properties Reflexive, symmetric, transitive, substitution, addition, subtraction, multiplication, division

B. Algebraic Properties Reflexive, symmetric, transitive, substitution, addition, subtraction, multiplication, division . efinitions 1) cute angle ) cute triangle 3) djacent angles 4) lternate exterior angles 5) lternate interior angles 6) ltitude of a triangle 7) ngle ) ngle bisector of a triangle 9) ngles bisector 10)

More information

Unit Activity Correlations to Common Core State Standards. Geometry. Table of Contents. Geometry 1 Statistics and Probability 8

Unit Activity Correlations to Common Core State Standards. Geometry. Table of Contents. Geometry 1 Statistics and Probability 8 Unit Activity Correlations to Common Core State Standards Geometry Table of Contents Geometry 1 Statistics and Probability 8 Geometry Experiment with transformations in the plane 1. Know precise definitions

More information

Mathematics II Resources for EOC Remediation

Mathematics II Resources for EOC Remediation Mathematics II Resources for EOC Remediation G CO Congruence Cluster: G CO.A.3 G CO.A.5 G CO.C.10 G CO.C.11 The information in this document is intended to demonstrate the depth and rigor of the Nevada

More information

Final Exam Review. Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of.

Final Exam Review. Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of. Final Exam Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the length of. 9 8 7 6 5 4 3 2 1 0 1 a. = 7 c. = 7 b. = 9 d. = 8 2. Find the best

More information

Geo 9 Ch 11 1 AREAS OF POLYGONS SQUARE EQUILATERAL TRIANGLE

Geo 9 Ch 11 1 AREAS OF POLYGONS SQUARE EQUILATERAL TRIANGLE Geo 9 h 11 1 RES OF POLYGONS SQURE RETNGLE PRLLELOGRM TRINGLE EQUILTERL TRINGLE RHOMUS TRPEZOI REGULR POLY IRLE R LENGTH SETOR SLIVER RTIO OF RES SME SE SME HEIGHT Geo 9 h 11 2 11.1 reas of Polygons Postulate

More information

Algebra Area of Parallelograms

Algebra Area of Parallelograms Lesson 10.1 Reteach Algebra Area of Parallelograms The formula for the area of a parallelogram is the product of the base and height. The formula for the area of a square is the square of one of its sides.

More information

Angle Unit Definitions

Angle Unit Definitions ngle Unit Definitions Name lock Date Term Definition Notes Sketch D djacent ngles Two coplanar angles with a coon side, a coon vertex, and no coon interior points. Must be named with 3 letters OR numbers

More information

Math 2 Plane Geometry part 1 Unit Updated January 13, 2017

Math 2 Plane Geometry part 1 Unit Updated January 13, 2017 Complementary angles (two angles whose sum is 90 ) and supplementary angles (two angles whose sum is 180. A straight line = 180. In the figure below and to the left, angle EFH and angle HFG form a straight

More information

First we need a more precise, rigorous definition:

First we need a more precise, rigorous definition: Lesson 21 Lesson 20, page 1 of 8 Glencoe Geometry Chapter 10.1 Polygons & Area We have been working with special types of polygons throughout the year. Rectangles, Squares, Trapezoids, and, yes, Triangles

More information

Classroom Assessments Based on Standards Geometry Chapter 1 Assessment Model GML201

Classroom Assessments Based on Standards Geometry Chapter 1 Assessment Model GML201 Classroom Assessments Based on Standards Geometry Chapter 1 Assessment Model GML201 Student Name: Teacher Name: ID Number: Date 1. You work for the highway department for your county board. You are in

More information

Indirect proof. Write indirect proof for the following

Indirect proof. Write indirect proof for the following Indirect proof Write indirect proof for the following 1.. Practice C A parallelogram is a quadrilateral with two sets of congruent parallel sides. The opposite angles in a parallelogram are congruent.

More information

Geometry Unit 5 - Notes Polygons

Geometry Unit 5 - Notes Polygons Geometry Unit 5 - Notes Polygons Syllabus Objective: 5.1 - The student will differentiate among polygons by their attributes. Review terms: 1) segment 2) vertex 3) collinear 4) intersect Polygon- a plane

More information

Geometry Fundamentals Midterm Exam Review Name: (Chapter 1, 2, 3, 4, 7, 12)

Geometry Fundamentals Midterm Exam Review Name: (Chapter 1, 2, 3, 4, 7, 12) Geometry Fundamentals Midterm Exam Review Name: (Chapter 1, 2, 3, 4, 7, 12) Date: Mod: Use the figure at the right for #1-4 1. What is another name for plane P? A. plane AE B. plane A C. plane BAD D. plane

More information

5. Trapezoid: Exactly one pair of parallel sides. 6. Isosceles Trapezoid is a trapezoid where the non-parallel sides are equal.

5. Trapezoid: Exactly one pair of parallel sides. 6. Isosceles Trapezoid is a trapezoid where the non-parallel sides are equal. Quadrilaterals page #1 Five common types of quadrilaterals are defined below: Mark each picture: 1. Parallelogram: oth pairs of opposite sides parallel. 2. Rectangle: Four right angles. 3. Rhombus: Four

More information

Unit 9: Quadrilaterals

Unit 9: Quadrilaterals Unit 9: Quadrilaterals Topic/Assignment I CAN statement Turned in? Properties of Quadrilaterals HW: Worksheet Properties of all Quadrilaterals Properties of Parallelograms HW: Properties of Parallelograms

More information

CORRELATION TO GEORGIA QUALITY CORE CURRICULUM FOR GEOMETRY (GRADES 9-12)

CORRELATION TO GEORGIA QUALITY CORE CURRICULUM FOR GEOMETRY (GRADES 9-12) CORRELATION TO GEORGIA (GRADES 9-12) SUBJECT AREA: Mathematics COURSE: 27. 06300 TEXTBOOK TITLE: PUBLISHER: Geometry: Tools for a Changing World 2001 Prentice Hall 1 Solves problems and practical applications

More information

Name Class Date. Lines that appear to be tangent are tangent. O is the center of each circle. What is the value of x?

Name Class Date. Lines that appear to be tangent are tangent. O is the center of each circle. What is the value of x? 12-1 Practice Tangent Lines Lines that appear to be tangent are tangent. O is the center of each circle. What is the value of x? 1. To start, identify the type of geometric figure formed by the tangent

More information

Wahkiakum School District, Pre-EOC Geometry 2012

Wahkiakum School District, Pre-EOC Geometry 2012 Pre-EO ssesment Geometry #2 Wahkiakum School istrict GEOM Page 1 1. Seth was supposed to prove PQR by SS for his homework assignment. He wrote the following proof: Given PRQ, PQ, and QR, then PQR by SS.

More information

Geometry SIA #3. Name: Class: Date: Short Answer. 1. Find the perimeter of parallelogram ABCD with vertices A( 2, 2), B(4, 2), C( 6, 1), and D(0, 1).

Geometry SIA #3. Name: Class: Date: Short Answer. 1. Find the perimeter of parallelogram ABCD with vertices A( 2, 2), B(4, 2), C( 6, 1), and D(0, 1). Name: Class: Date: ID: A Geometry SIA #3 Short Answer 1. Find the perimeter of parallelogram ABCD with vertices A( 2, 2), B(4, 2), C( 6, 1), and D(0, 1). 2. If the perimeter of a square is 72 inches, what

More information

Mathematics Standards for High School Geometry

Mathematics Standards for High School Geometry Mathematics Standards for High School Geometry Geometry is a course required for graduation and course is aligned with the College and Career Ready Standards for Mathematics in High School. Throughout

More information

Slope Station. 2. When are two lines in the plane perpendicular to one another?

Slope Station. 2. When are two lines in the plane perpendicular to one another? Slope Station 1. When are two lines in the plane parallel to each other? When their slopes are equal 2. When are two lines in the plane perpendicular to one another? When their slopes are opposite reciprocals

More information

Geometry: A Complete Course

Geometry: A Complete Course Geometry: omplete ourse with Trigonometry) Module Instructor's Guide with etailed Solutions for Progress Tests Written by: Larry. ollins RRT /010 Unit V, Part, Lessons 1, uiz Form ontinued. Match each

More information