GEOMETRY FINAL REVIEW FALL 2016Name Period

GEOMETRY FINAL REVIEW FALL 2016Name Period

1. Which points are collinear? Which points are coplanar?

2. Name the intersection of planes TUCO and TURG.

3. What ray is opposite ?

4. If M is the midpoint of , find x.

5. If bisects , find x.

6. ABC and CBD are supplementary angles, mABC = 4x +10, and mCBD = 6x + 20.

Solve for x. What is mABC?

7. The endpoints of are A(8, ‒2) and T(–8, 12). Find the midpoint of .

8. What is the distance between A(‒5, 4) and B(1, ‒4)?

9. What is the circumference of the circle with radius 4.1? Leave your answer in terms of .

10. All angles in the given figure are right angles. What is the area of the figure?

11. What is the next term of this sequence? 5, 8, 11, 14, 17, 20 ...

12. What is the converse of the given statement?

If Teresa fails her vision test, then she will order glasses.

13. What is the contrapositive of the given statement?

If Vanessa finds a job, then she will go on a shopping spree.

14. Conditional: If a triangle is equilateral, then the triangle has three congruent sides.

Write as a true biconditional.

15. Write a valid conclusion, assuming the following statements are true.

If a polygon is a regular hexagon, then the polygon has exactly six congruent sides.

The polygon is a regular hexagon.

16. Using the transitive property of equality, if ?

17. Name the property of equality that justifies the statement: .

18. and are complementary. If and , what is the value of ?

19. and are vertical angles. & . Solve for x. What is the measure of ?

20. In the figure, if, and , what is ?

For Questions 21-22, refer to the figure below.

21. Identify the plane parallel to plane HIGF.

22. Identify four segments which are skew to ?

For Questions 23-25, refer to the figure at the right.

23. Identify the special name for each angle pair :

∠ 4 and ∠ 8∠ 2 and ∠ 7∠ 3 and ∠ 5∠ 4 and ∠ 5

24. Given a ║ b and m∠ 2 = 61°, find m∠ 6.

25. Given a ║ b, m∠ 4 = 5x + 100, and m∠ 6 = 7x + 20, find the value of x.

26. Find the slope of the line that contains (–4, 3) and (10, 5).

27. Write an equation of the line with slope that contains (4, – 8) in point slope form.

28. Write an equation of the line containing (2, –3) and (6, 17) in slope intercept form.

29. Given the figures, describe each triangle

a) by angles and b) by sides

30. Solve for x, y and z.

31. Complete the proof.Given: L is the midpoint of , ∥

Prove: △JKL ≅ △MNL

32. Given the equations of the lines and ,

are these lines parallel, perpendicular or neither?

33. If , then BC = ____.

34. Can the two triangles be proved congruent? If so, by which method?

35. Complete the proof.Given: , AC = EC

Prove: C is the midpoint of

36. Find the value of x.

37. Find the value of x.

38. Find the value of x.

39. Find the value of x.

40. Z is the centroid of ABC. If CZ = 8, what is ZX?

41. What is the best description of for each triangle?

42. What is the best description of B and P?

43. What is the first step of the following indirect proof?

Given: The side lengths of a triangle are 4, 4, and 6.

Prove: The triangle is not a right triangle.

44. Could the following lengths be the sides of a triangle?

3, 4, 66, 7, 137, 9, 17

45. Lists the angles in order from the smallest to the largest.

46. What are the possible lengths for x, the third side of a triangle, if two sides are 5 and 11?

47. Write an inequality relating LP and XA.

48. What is the sum of the interior angle measures of a regular pentagon?

49. What is the measure of one interior angle of a regular 15-gon?

50. If the exterior angle of a regular polygon is 15°, how many sides does the polygon have?

51. Solve for s in this parallelogram. What is ?

52. For what value of x must ABCD be a parallelogram?

53. How can you prove that a quadrilateral is a rhombus?

54. ABCD is a rectangle. If AC = 6x + 2 and BD = x + 22, find the value of x.

55. In the isosceles trapezoid at the right, what is the measure of

56. For this rhombus, what is the measure of

57. Given the kite, find the measure of

58. Sketch the construction of the bisector of A. A

59. Sketch the construction of the perpendicular bisector of B C

60. Sketch the construction of a line perpendicular to k through P. k

61. Sketch the construction of a line perpendicular to m through R. m