8. T(3, 4) and W(2, 7) 9. C(5, 10) and D(6, -1)

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1 Name: Period: Chapter 1: Essentials of Geometry In exercises 6-7, find the midpoint between the two points. 6. T(3, 9) and W(15, 5) 7. C(1, 4) and D(3, 2) In exercises 8-9, find the distance between the two points. 8. T(3, 4) and W(2, 7) 9. C(5, 10) and D(6, -1) 10. The ray!" bisects $!% and LOM is 21. Draw a picture to determine the measure of $!% is a complement of 2 and 1 = 5. What is the measure of 2? is a supplement of 2 and 1 = 5. What is the measure of 2?

2 13. A complementary pair of angles have the measurements (x -10) and (2x + 40) Find the measures of each of the angles. 14. Use the exterior angle theorem to find x. Chapter 2: Reasoning and Proof Hypothesis- Conclusion- 15. Write the converse, inverse and the contrapositive for the given statement. a.) If an animal is a frog, then it is an amphibian. -Converse: -Inverse: -Contrapositive:

3 Chapter 3: Parallel and Perpendicular Lines 16. Write an equation of the line that passes through the given point P (-2, 4) and has the slope m = ) Write an equation of the line that passes through point P (-1, 1) and is parallel to the equation y = 2x ) Write an equation of the line that passes through point P and is perpendicular to the equation. P (3, 4), 0 = Chapter 4: Congruent Triangles 19. What are the five congruency postulates? 20. Tell whether the triangles can be proven congruent by the given postulate. a.) b.) c.)

4 Chapter 5: Relationships with Triangles 21.) Is it possible to construct a triangle with the given side lengths? a. 4, 11, 15 b. 3, 11, 15 c. 5, 11, 15 Chapter 6: Similarity 22) What are the triangle similarity postulates? 23) Determine which similarity theorem or postulate proves the triangles below are similar. Choices: AA Postulate, SSS Similarity theorem, SAS Similarity theorem a) b) 24. Use the diagram where 789 ~ ;<=. a.) Write a proportion to show which sides are similar. b.) Find the value of x. 25) If ΔAEB ΔADC, what is the value of AB?

5 ***Chapter 7: Right Triangles and Trigonometry 26.) Draw a right triangle. Label the right triangle with leg lengths 7 and 14. Find the hypotenuse in radical form. 27) Is this a Pythagorean triple 10, 11, 14? 28) How can you determine whether a triangle is acute, right, or obtuse? 29) Which type of triangle is formed with side lengths 10, 11, 14? (Lesson 7.2) 30) Find the value of x. Write your answer in simplest radical form. 31) What is the relationship between the sides of a triangle? 32) What is the relationship between the sides of a triangle?

6 33). Find the value of each variable. Write your answer in simplest radical form. a.) b) c) d) 34.) Using SOH-CAH-TOA a) Find AC. b) Find cos C. c) Find sin C. d) Find tan A. 35.) Using SOH-CAH-TOA a) Find mgh. (show your work)

7 Chapter 8: Quadrilaterals 36. Three interior angles of a quadrilateral are 52, 104, and 128. What is the measure of the fourth angle? 37. What is the sum of the interior angles of a regular hexagon? What is the measure of one interior angle of a hexagon? (see formula sheet) 38) How can you tell that a quadrilateral is a parallelogram? a) b) 39. Solve for x given the following parallelogram. 40. Solve for the values of w, x, y and z in the parallelogram.

8 41. Find m M. 42. Find m G 43. Find the midsegment of the trapezoid. 44 & 45) How can you tell that a parallelogram is a rhombus? Square? ***Chapter 10: Properties of Circles 46. Use the diagram at the right to label c) C@ d) point B e) DE 47. Find m FG and mhgf

9 48. Use properties of tangents to solve for the variable. a. b.) 49. Use properties of chords to solve for the x and y. 50. Use properties of inscribed angles to find mi% and mij a) 51) Use properties of inscribed polygons to find m TUV

10 52. Use angle relationships (see formula sheet) to find a) m 1, b) x, and c) x 53. Use segment lengths (see formula sheet) to find x. Chapter 11: Measuring Length and Area 54. Find the area of the polygons (use formula sheet). a.) b)

11 55. Find the area of a parallelogram with a base of 30 and a height of The lengths of the diagonals of a kite are 67 and 41 cm. What is the area? 57. A right triangle has a hypotenuse of 17 cm and a height of 8 cm. Find the length of the other leg, and then find the area of the triangle. 58. The area of a rectangle is 100 square units. If the length is 4 times the width, find the value of the length and the width. 59. Find the circumference and area of a circle with a diameter of 22cm. 60. Find the approximate radius of a circle with a circumference of 90 meters.

12 Chapter 12: Surface Area and Volume of Solids 61. Find the surface area of the following geometric solids. (Use formula sheet) a) b) c) 62. Find the volume of the following geometric solids. (Use formula sheet) a) b) c) d) e) hemisphere

Geometry SOL Study Sheet. 1. Slope: ! y 1 x 2. m = y 2. ! x Midpoint: + x y 2 2. midpoint = ( x 1. , y Distance: (x 2 ) 2

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