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GEOMETRY FALL
FINAL REVIEW
Name_________________________Per______
1. Find the length of ̅̅̅̅
𝐵𝐶 .
For Exercises 2-4, use the figure at the right.
2. Which point is the vertex of all the angles in this figure?
3. What type of angle is ∠ ABC?
4. What is m∠ EBF ?
5. Which three points in the figure are non-collinear?
6. Find the distance between P(2, 7) and Q(5, 3).
7. Find the coordinates of the midpoint of ̅̅̅̅
𝐿𝐵 if L(10, 5) and B(–6, 2).
8. Find the value of x if S is between R and T, RS is x + 2, ST is 4x, and RT is 57.
For Exercises 9–10, use the figure at the right.
9. Name a pair of angles that are supplementary?
10. Which angle is a vertical angle to ∠ WSR ?
11. Describes this figure by name, convex or concave, and regular or not regular.
12. Make a conjecture about the next term in this sequence: 98, 94, 90, 86, 82.
13. Identify the hypothesis of the statement If x + 6 = 10, then x =4.
14. Identify the converse of the statement If birds fly, then dogs bark.
15. Identify the inverse of the statement If a triangle has 2 equal sides, then it is isosceles.
16. Is the statement A plane contains at least 3 points not on the same line always, sometimes or never true?
For Exercises 17-18, state the property that justifies the statement.
17. If x – 6 = 10, then x = 16.
̅̅̅̅ ≅ 𝑊𝑋
̅̅̅̅̅ , then PS = WX.
18. If 𝑃𝑆
19. If A, B, and C are collinear and AB + BC = AC, which point is between the other two points?
20. Find the value of x.
21. If m∠ ABD = 66, find m∠ DBC.
For Questions 22-23, refer to the figure at the right.
22. Identify the plane parallel to plane AEF.
23. Which segment is skew to AB ?
For Questions 24-26, refer to the figure at the right.
Identify the special name for each angle pair.
24. ∠ 2 and ∠ 7
25. Given a ║ b and m∠ 2 = 68, find m∠ 6.
26. Given a ║ b, m∠ 3 = 2x + 10, and m∠ 5 = 3x + 10, find the value of x.
27. Determine the slope of the line that contains (–6, 2) and (10, 9)
28. Given A(–1, 4), B(1, 5), and C(–5, 1), which coordinate will make ̅̅̅̅
𝐴𝐵 parallel to ̅̅̅̅
𝐶𝐷 ?
̅̅̅̅ perpendicular to 𝐶𝐷
̅̅̅̅ ?
29. Given A(2, 3), B(6, 7), and C(5, 1), which coordinate will make 𝐴𝐵
1
30. Write an equation of the line with slope 2 that contains (–3, 5) in point slope form.
31. Write an equation of the line through (2, –3) and (6, 15) in slope intercept form.
32. Describes the type of triangle?
33. What is m∠ 2?
34. Which triangles are congruent in the figure?
35. If △CJW ≅ △AGS, m∠ A = 50, m∠ J = 45, and m∠ S = 8x + 5, what is the value of x?
Use the proof for Questions 36 and 37.
Given: L is the midpoint of ̅̅̅̅
𝐽𝑀
̅̅̅
𝐽𝐾 ∥ ̅̅̅̅̅
𝑁𝑀
Prove: △JKL ≅ △MNL
Statements
Reasons
1. L is the midpoint of ̅̅̅̅̅
𝐽𝑀 .
̅
̅̅̅̅
2. 𝐽𝐿 ≅ 𝑀𝐿
3. ̅̅̅
𝐽𝐾 ∥ ̅̅̅̅̅
𝑀𝑁
4. ∠ JKL ≅ ∠ MNL
5. ∠ JLK ≅ ∠ MLN
6. △JKL ≅ △MNL
1. Given
2. Definition of midpoint
3. Given
4. Alt. int.
are ≅.
5. (Question 9)
6. (Question 10)
36. What is the reason for ∠ JLK ≅ ∠ MLN?
37. What is the reason for △JKL ≅ △MNL?
38. What are the lengths of the sides of this equilateral triangle?
̅̅̅̅ ?
39. If △DJL ≅ △KMS, which segment in △KMS corresponds to 𝐷𝐿
39. Which triangles are congruent in the figure?
41. The rhombus QRST is made of two congruent isosceles triangles. Given m∠ QRS = 36,
what is the measure of ∠ S?
42. Name the shortest side of △DEF.
43. Which angle in △ABC has the smallest measure?
44. If D is the circumcenter of △ABC and DB = 4, find DA.
45. Choose the assumption you would make to start an indirect proof.
Given: a ∦ b
Prove: ∠ 1 and ∠ 2 are not congruent.
46. Can the sets of numbers 5, 5, 10 can be the lengths of the sides of a triangle?
For Questions 47-49, refer to the figure to determine which is a true statement for the given information.
47.
̅̅̅̅̅
𝑌𝑊 is an angle bisector.
48.
̅̅̅̅̅ is an altitude.
𝑌𝑊
49.
̅̅̅̅̅
𝑌𝑊 is a median.
50. What is the relationship between the lengths of ̅̅̅̅
𝐷𝐶 and ̅̅̅̅
𝐴𝐷 ?
51. What is the relationship between the measures of ∠ 1 and ∠ 2?
52. Find the sum of the measures of the interior angles of a convex 20-gon.
53. Find the sum of the measures of the exterior angles of a convex 31-gon.
54. For parallelogram ABCD, find the value of x.
55. List the properties of a parallelogram?
56. List the properties of a rectangles?
57. Name a pair of base angles of trapezoid ABCD.
58. ABCD is a rectangle. If AC = 5x + 2 and BD = x + 28, find the value of x.
59. For rhombus GHJK, find m∠ 1.
60. The length of one base of a trapezoid is 23 inches and the length of the
median is 16 inches. Find the length of the other base.
61. For kite PQRS, find m∠ Q.
62. The incenter of a circle is the intersection of the
.
63. To circumscribe a circle, you must construct the
.
64. Sketch a construction of a perpendicular bisector?
65. Sketch a construction of an angle bisector?
66. Which construction would you use to construct the midpoint of a segment?
67. Which construction would you use to construct the altitude of a triangle?