Geometry L1 2017 Midterm Topic List Unit 1: Basics of Geometry 1. Point, Line, Plane 2. Segment Addition Postulate 3. Midpoint Formula, Distance Formula 4. Bisectors 5. Angle Pairs Unit 2: Logical Reasoning 1. Conditional Statements 2. Bi-Conditional Statements 3. Properties of Equality 4. Algebraic Proof 5. Segment and Angle Proofs Unit 3: Types of Lines 1. Parallel Lines 2. Perpendicular Lines 3. Angles Pairs 4. Slopes of parallel and perpendicular lines 5. Proving Lines parallel In addition to reviewing all quizzes, test, homework, notes, assigned throughout the first semester. Students should always study by doing additional problems. The following packet consists of skillbased problems by chapter. In order to be successful on the Midterm Exam, students also need to know Geometry vocabulary, notation, theorems, and formulas Unit 4: Triangle Congruence 1. Classifying Triangles by their angles and sides 2. Triangle congruence SAS, SSS, ASA, AAS, HL, CPCTC 3. Triangle Sum Theorem, Exterior Angle Theorem Unit 5: Properties of Triangles 1. Points of Concurrency 2. Midsegments, Perpendicular Bisectors, Angle Bisectors, Medians Geometry L1 2017 Midterm Outline (120 points) I. 25 Multiple Choice (25pts) II. 10 True & False (10pts) III. 15 Matching (15pts) IV. 12 Short Answer (42pts) V. 3 Proofs (18pts) VI. 10 Common Assessment (10pts) 1
I. Geometric Reasoning (Units 1 & 2) Circle the best answer. 1. If two planes intersect, then they intersect in exactly one. A segment B line C point D ray 2. Which is an alternative name for LN? A L B NL C LK D LM 3. What is the distance between the points (6, 7) and (1, 5)? A 13 B 53 C 13 D 119 4. W is the midpoint of VX. What is VX if VW = 2x + 5 and WX = 4x 3? A 4 B 13 C 8 D 26 5. Which is NOT a name for the angle at the right? A P B QPR C PQR D RPQ 6. JK bisects LJM, which is an obtuse angle. What is the greatest possible whole-number measure of LJK? A 99 B 90 C 91 D 89 7. Which completes the sentence? 1 and 2 are angles. A adjacent B complementary C supplementary D vertical 8. KLM and RST are complementary angles. m KLM = (7x) and m RST = (36 x). What is the measure of the smaller angle? A 9 B 30 C 27 D 63 2
9. What is the circumference to the nearest tenth of a millimeter, of a circle whose radius is 40 mm? A 62.8 mm B 188.5 mm C 125.6 mm D 251.3 mm 10. What is the area of a square whose sides measure (x 8)? A 2x 16 B x 2 64 C 4x 32 D x 2 16x + 64 11. The midpoint of a segment is ( 9, 1). One endpoint of the segment is (2, 5). What are the coordinates of the other endpoint of the segment? A ( 16, 7) B (13, 9) C ( 20, 3) D ( 5, 6) 12. To the nearest tenth of a unit, what is the distance between (4, 5) and ( 8, 1)? A 4 10 B 16 10 C 11.3 units D 4.5 units 13. Which transformation can you perform on the point (1, 10) to obtain ( 1, 10) as the image? A reflection over the x-axis B reflection over the y-axis C a rotation of 90 D a rotation of 180 14. What is the image of (6, 7) after a reflection over the y-axis? A (6, 7) B ( 6, 7) C (6, 7) D ( 6, 7) 15. Which is a counterexample to the conjecture All prime numbers are odd? A 0 B 3 C 2 D 4 16. Which is the hypothesis of the conditional statement If a triangle is an obtuse triangle, then two of its angles are acute. A If B a triangle is an obtuse triangle C then D two of its angles are acute 17. Which is the contrapositive of the statement If a line bisects a segment, then it divides the segment into two congruent segments? A If a line divides a segment into two congruent segments, then it bisects the segment. B If a line does not bisect a segment, then it does not divide the segment into two congruent segments. C If a line does not divide a segment into two congruent segments, then it does not bisect the segment. D If a line does not divide a segment into two congruent segments, then it bisects the segment. 3
18. If k 8 = 0, what property justifies k = 8? A Distributive Property B Transitive Property of Equality C Addition Property of Equality D Subtraction Property of Equality 19. Complete: By the Multiplication Property of Equality, if a = b, then. A ab = ba B ac = bd C ac = bc D ab = ab 20. Given: If a square has an area of 36 square units, then its perimeter is 24 units. Which is a related biconditional statement for the given statement? A If a square has a perimeter of 24 units, then it has an area of 36 square units. B The perimeter of a square is 24 units if and only if it has an area of 36 square units. C If a square does not have a perimeter of 24 units, then it does not have an area of 36 square units. D If a square does not have an area of 36 square units, then it does not have a perimeter of 24 units. 21. Given: 1 and 2 are supplementary; 1 2 Prove: 1 is a right angle. In a two-column proof, which is the statement in the final step? A Right Angle Congruence Theorem B 1 and 2 are supplementary. C 1 is a right angle. D Definition of right angle 22. Two angles form a linear pair. One angle measures (10x 63) o. The other angle measures (8x) o. What is the value of x? A 8.5 B 31.5 C 13.5 D Cannot be determined 23. If n 7 7 =, which justifies the statement n = 3 6 2? A Substitution B Reflexive Property of Equality C Division Property of Equality D Multiplication Property of Equality 4
II. Parallel and Perpendicular Lines (Unit 3) Part I. Circle the best answer. 1. Which statement is NOT true? A Parallel lines do not intersect. B A segment has exactly two endpoints. C Two planes that do not intersect are always skew. D A ray has exactly one endpoint. 2. How many different rays can be named using three collinear points P, Q, and R? A 6 B 3 C 2 D 4 3. The midpoint of XY is Z. If XY = 3n and XZ = n + 15, what is YZ? A 18 B 45 C 36 D 90 4. In the figure, what is RS? A 5 B 56 C 32 D 70 5. In degrees, what is m 1? A 76 B 108 C 104 D 156 6. The measures of two supplementary angles are (3x 10) o and (6x + 100) o. In degrees, what is the measure of the smaller angle? A 0 B 20 C 10 D 7. What is the area of a rectangle whose sides measure 2g and (g + 5)? 2 26 3 A 3g + 5 B 6g + 10 C 6g + 5 D 2g 2 + 10g 8. To the nearest whole number, what is the circumference of a circle whose radius is 12.5? Use 3.14 for π. A 20 B 79 C 39 D 491 5
9. The midpoint of VW is P(4, 3). If the coordinates of W are (0, 15), what are the coordinates of V? A (8, 21) B (4, 33) C ( 8, 21) D (2, 6) 10. What is the distance from (8, 1) to (3, 11) on the coordinate plane? A 13 units B 24 units C 13 units D 34 units 11. What are the coordinates of the image of K( 8, 7) after the translation (x, y) (x 10, y 2)? A ( 18, 5) B (18, 5) C (2, 9) D ( 2, 9) 12. Which transformation maps T( 6, 3) to T (6, 3)? A 90 o rotation B 180 o rotation C reflection over the x-axis D reflection over the y-axis 13. Which is a counterexample that disproves the conjecture If the area of a rectangle is 36 square units, then the perimeter is less than 36 units? A a 6 by 6 rectangle B a 4 by 9 rectangle C a 3 by 12 rectangle D a 2 by 18 rectangle 14. Which conditional statement is true? A If it is raining outside, then the ground is wet. B If a person lives in the United States, then the person lives in Chicago. C If a number is divisible by 3, then the number is odd. D If today is Saturday, then yesterday was Sunday. 15. What is the converse of the statement If the key fits, then the lock opens? A If the lock does not open, then the key does not fit B If the lock opens, then the key fits. C If the key does not fit, then the lock does not open. D If the key fits, then the lock does not open. 16. Given: If Maria passes geometry, then she will graduate. Maria passes geometry. What can you conclude? A Maria will take geometry. B If Maria does not graduate, then she is not taking geometry. C If Maria does not take geometry, then she will graduate. D Maria will graduate. 6
17. Which is a biconditional statement for the given conditional? If two coplanar lines do not intersect, then they are parallel. A Two coplanar lines intersect if and only if they are not parallel. B Two coplanar lines do not intersect if and only if they are parallel. C Two coplanar lines are not parallel if and only if they intersect. D Two coplanar lines intersect if and only if they are parallel. 18. Which biconditional statement is true? A Peter lives in Cincinnati if and only if he lives in Ohio. B A rectangle has sides 3 and 5 if and only if its area is 15. C Two segments are congruent if and only if they have the same measure. D Two angles measure 90 o if and only if they are supplementary. 19. If 6k 9 = 20 and k = r, why is 6r 9 = 20? A Addition Property of Equality B Multiplication Property of Equality C Symmetric Property of Equality D Substitution Property of Equality 20. Which property justifies the statement If 2y = n and n = 3, then 2y = 3? A Transitive Property of Equality B Reflexive Property of Equality C Symmetric Property of Equality D Multiplication Property of Equality Refer to the figure for Exercises 21 and 22. 21. Which pair of angles are corresponding angles? A 1 and 2 B 1 and 4 C 1 and 3 D 1 and 6 22. Which completes the statement Angles 6 and 7 are an example of angles? A same-side interior B alternate interior C alternate exterior D corresponding 23. If lines p and q are parallel, what is the value of x? A 15 B 45 C 30 D 90 7
24. If j k, which could be one of the angle measures? A 25 o C 37 o B 60 o D 84 o 25. If x = 7, which lines must be parallel? A r s only C r t only B s t only D r s t 26. Which angle must be congruent to 8 to prove that u v? A 1 C 2 B 3 D 4 27. Which inequality must be true, given the information in the figure? A x < 3 C x > 3 B 2 > x D x < 3 28. In the figure, ABD CBD. What is the value of x? A 6 B 30 C 24 D 48 29. What is the slope of the line whose equation is 2x 6y = 0? A 1 B 2 1 C 3 3 3 D 3 30. What is the slope of a line parallel to the graph of y + 1 = 8(x 2)? A 8 B 1 2 C 2 D 1 8 8
31. Which is an equation of the line in the graph? 2 y + 4 = ( x 3) A 3 B y + 3 = 2 ( x 4) 3 C y 4 = 2 ( x + 3) 3 D y 3 = 2 ( x + 4) 3 32. The graph of y = 3x 8 coincides with the graph of 6x ay = 16. What is the value of a? A 2 B 1 C 1 D 2 Part II. Answer each below. 1. Identify a pair of skew segments. 2. Write True or False. Perpendicular lines cannot be skew lines. 3. How many total pairs of both alternate exterior and alternate interior angles are formed by a transversal that intersects two coplanar lines at two different points? Use the figure below to answer questions 4 and 5 4. Given: 8 and 6 are corresponding angles. Identify the transversal. 9
5. If 1 is an alternate exterior angle, name two other angles that are alternate exterior angles with it. 6. If parallel lines are intersected by a transversal that is not perpendicular to them, how many pairs of nonadjacent supplementary angles are formed? 7. What one word completes the following sentence? angles formed by a transversal of parallel lines are congruent and all the angles are supplementary to all the obtuse angles. 8. Find the measure of QRS and state the postulate or theorem that justifies your answer. 9. If 1 6 and m 1 90 o, is r s? 10. Which values for x and y make lines r, s, and t parallel? 10
11. If two parallel lines and a transversal form angles that are all congruent, describe the relationship between the transversal and each of the parallel lines. 12. Write and solve an inequality for x. 13. If the slope of a line is 0, which type of line is it and what is true about the y-coordinates of all points on the line? 14. If line r through (1, 1) and (5, 7) is parallel to line s through (4, 2) and (x, y), what are possible values for x and y? 15. Write True or False. All horizontal lines are perpendicular to all vertical lines, so the product of the slope of a horizontal line and the slope of a vertical line is 1. 16. Write True or False. Multiplying both sides of the equation for a line by the same nonzero number will produce an equation for a line that coincides with the original line. 17. Write the equation in point-slope form of the line that passes through (4, 3) and is parallel to y = 2x + 7. 18. Write an equation in slope-intercept form for the line that passes through (6, 10) and is perpendicular to 2x + 3y = 6. 11
III. Triangle Congruence (Unit 4) Part I. Circle the best answer. 1. Describe the transformation M: (x, y) (-y, x). A A reflection across the y-axis. B A reflection across the x-axis. C A rotation 90 o clockwise with center of rotation (0, 0). D A rotation 90 o counterclockwise with center of rotation (0, 0). 2. Which best describes ABC with vertices A( 2, 1), B(0, 4), and C(2, 1)? A acute B obtuse C equiangular D right 3. Which is a correct classification of DEF with vertices D( 3, 2), E( 2, 3), and F(1, 0)? A equilateral B scalene C isosceles D Not here 4. What is the value of x? A 41 B 99 C 58 D 122 5. QRS STQ, QS = x 2 10 and SQ = 2x 2. What is the value of x? A 4 B 2 C 2 D 4 6. Given: ABC with vertices A(5, 2), B(5, 7), and C(1, 2). Which set of coordinates best repositions the triangle to make a coordinate proof easier? A (0, 0), (4, 0), and (4, 5) B (0, 0), ( 4, 0), and (0, 5) C (0, 0), (0, 4), and (5, 0) D (0, 0), (4, 0), and (0, 5) 11
Use the figure for Exercises7 9. 7. What information would allow you to prove AED CEB by SAS? A E is the midpoint of DB. B E is the midpoint of AC. C E bisects AC. D E bisects both DB and AC. 8. If ADC and ABC are right angles, AC = BD, and AB = DC, which postulate or theorem proves ABC CDA? A SSS B ASA C SAS D HL 9. If AD BC and ABD CDB, which postulate or theorem could be used to prove ABD CDB? A SAS B SSS C ASA D HL 10. If the height of a right triangle is n units and the base is m units, which statement is NOT true? A The midpoint of the hypotenuse is (m, n). B A(0, 0), B(m, 0), and C(0, n) can represent the vertices. m n C The midpoint of the hypotenuse is,. 2 2 D The slope of the hypotenuse is n m. 11. What is m DAC? A 30 B 60 C 45 D Not here 66
Use the partially completed two-column proof for Exercises 12 and 13. Given: JK Prove: JY LK LX ; JYL and LXJ are rt. s. Proof: Statements Reasons 1. KJL KLJ 1.? 2. JL LJ 2.? 3. JYL and LXJ are rt. s. 3. Given 4. JYL LXJ 4.? 5. JYL LXJ 5.? 6. JY LX 6.? 12.Which justification belongs in Step 1? A Base Angles Theorem. B Reflex. Prop. of C Right Theorem. D CPCTC 13. Which justification belongs in Step 5? A ASA B AAS C HL D SSA Part II. Answer each below 1. Prove by mathematical calculation that triangles F(4, 6), G(5, 7),H(7, 4) and J(1, -4), K(2, -5), L(4, -2) are congruent. 13
Use the figure for Exercises 2 and 3. 2. Classify ABC by angle measures. 3. Classify ABD by side lengths. Use the figure for Exercises 4 and 5. 4. What is m T? 5. What is the value of y? 6. Given QRS STQ, R = 4x 2 4, and T = 3x 2 3x. What is m R? 7.Given QRS STQ, RS = 3x 3, TQ = 2x + 2, and QR = x 2 2. What is the length of side ST? 8. What is the value of x? 15
Use the figure for Exercises 9 12. 9. If AD BC, write a statement about point E that would allow you to prove AED CEB by the SSS Postulate. 10. Suppose AE CE and BE DE. What postulate or theorem will allow you to prove that BEA DEC? 11. DAB and BCD are right angles. Write a single congruence statement about two segments that would allow you to conclude that DAB BCD. What theorem or postulate would justify the conclusion? 16
IV. Properties and Attributes of Triangles (Unit 5) Part I. Circle the best answer. 1. AC is the perpendicular bisector of BD. What is the value of x? A 2.4 B 2 6 3 C 4 D Not here 2. In the figure at the right, what is m XYZ? A 70 o B 145 o C 125 o D Not here 3. Which is the radius of a circle inscribed in KLM? A the distance from the incenter to a side of the triangle B the distance from the circumcenter to a side of the triangle C the distance from the incenter to a vertex of the triangle D the distance from the circumcenter to a vertex of the triangle 4. ABC is the midsegment triangle of TUV. Which measure CANNOT be determined? A m VAC C m TAC B m CBT D m AVC 5. PQ is the midsegment of GHK, and GH is the midsegment of KLM. What is the length of PK? A 4 B 14 C 7 D 28 6. The length of a leg of a right triangle is two times the length of the other, and the hypotenuse is 25. What is the length of the longer leg? A 2 5 B 5 C 10 5 D 25 17
7.What is the value of x? A 5 2 B 2 5 C 25 5 D 25 3 Part II. Answer each below. 1. In ABC, B is on the perpendicular bisector of AC, m A = (6x + 14) o, and m ABC = (10x 2) o. Find m C. 2. Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints (2, 4) and (6, 2). 3. Find m DEF. 4. TG and GV are angle bisectors of TUV. Find m VGT and the distance from G to UV. 5. Find the value of x. 18
6. What is m TAC? 7.List the angles of KLM with vertices K( 2, 2), L(2, 6), M(7, 2) in order from smallest to largest. 8.Determine the side lengths of the triangle. 19