Geometry 1st Semester Final Review

1. A plane is determined by ….

2. The three undefined terms in geometry are ….

3. If H is the midpoint of and TH = 11.22, then TE = .

4. What is the measure of ?C D E4x + 8 27

6x

5. Draw a plane with intersecting lines r and s and line s contains three collinear points A, B, C.

6. Solve: 2(4x – 3) –8 = 4 + 2x

7. M is the interior of TOP. If mTOM = 12.5 and mMOP = 16.5, then mTOP = .

8. bisects ABC, m ABD = (7x – 1) , and m DBC = (4x + 8) . Find m ABD.

9. Use inductive reasoning to determine the next three numbers in the following sequence:

1, -3, 5, -7, 9, …

10. What three items are next in the pattern?

11. Evaluate when s=5 and r=1

12. Use the distance formula to find BN.

B

N

1 2 3 4 5 6 7–1–2–3–4–5–6–7 x

1

2

3

4

5

6

7

–1

–2

–3

–4

–5

–6

–7

y

13. Given with endpoints G(-6, -6) and H(1, 2), what are the coordinates of the midpoint?

14. What is the slope of the line through (7, 6) and (3, -2)?

15. Sketch a line that would have a negative slope.

16. Sketch a line that would have a positive slope.

17. Sketch a line that would have a zero slope.

18. Sketch a line that would have a undefined slope.

19. Write an equation of a line perpendicular to

y = x + 4?

20. What is the equation of the line though (-1, 7) and (4, -3)?

21. Write an equation of a line parallel to

y = x + 2?

22. Determine whether the pair of lines 12x + 3y = 3 and y = 4x + 1 are parallel,intersect, or coincide.

23. l1 || l2, then …

which angles are corresponding angles and what is their property?

which angles are alternate interior angles and what is their property?

which angles are same side interior angles and what is their property?

24. l1 || l2, find m1, if the m2 = 6x + 26, and m4 = 2x + 10.

25. Find the measure of the complement of M, where m M = 32.626. Find the measure of the supplement of R, where m R = 132.6

27. Identify the hypothesis and the conclusion of the conditional statement.

If it is raining, then the sun is not shining.

H:

C:

28. Write the logic symbolism for;

conditional statement:

converse statement:

inverse statement:

contrapositive statement:

biconditional statement:

law of syllogism:

29. Simplify the following ( a - e ):

a)

b)

c)

d)

e) 30. Write the converse, inverse, and contrapositive of the conditional statement:

If it is a horse, then it has 4 legs.

converse statement:

inverse statement:

contrapositive statement:

31. Classify ∆DAB by its angle measures, given mDAB = 56 and mABD = 72 .

32. Classify ∆DBC by its angle measures, given mBDC = 26 and mDCB = 51 .

33. ∆ABC is an isosceles triangle. is the shortest side with length 3x + 9.

BC = 8x – 8 and CA = 3x + 27. Find AB.

34. One of the acute angles in a right triangle has a measure of 41.7°. What is the measure of the other acute angle?

35. Given that ∆ABC ∆DEC and mE = 47º, find mACB.

36. What is the m CBA, if m CAB = 26?

37. What is the value of x, if m CBA = 6x?

38. What is the mACD, if mABC = 37 ?

39. AB = 16.5, AX = 7.9, and BC = 16.5. What is the length of ?

40. The circumcenter is equidistant from

the of a triangle?

41. The orthocenter of a triangle is the point of concurrency of which lines?

42. The incenter is equidistant from the

of a triangle?

43. Write a congruence statement for these triangles, and name the postulate or theorem that supports it.

44. Write a congruence statement for these triangles, and name the postulate or theorem that supports it.

45. What can you use to prove ABE CDE.

46. Classify and .

47. Given: TUV TWV. What is the value of x?

48. List the sides of ABC in order from shortest to longest?

49. . List the angles of GHJ in order from smallest to largest?

50. Find the measure of ‘x’.

122

x

51. Find the measure of ‘x’.

2x - 5

3x - 17

x + 40

5550

75

A

B

C

52. Find the measure of BCA.

53. In ∆ABC, ZC, YB, and XA are the medians of the triangle. BY = 6.6, find BO.

X

A

Y

B Z

C

O

54. Given that bisects XYZ and WZ = 14.3, find WX.

55. Tell whether a triangle can have sides with lengths 4, 2, and 7.

56. and are angle bisectors of ∆JHI.

Find m .

57. and are angle bisectors of ∆JHI.

Find the distance from K to .

58. What is the orthocenter of this triangle?

59. Find the values of x and y. Express your answers in simplest radical form.

60. Find the value of x. Express your answer in simplest radical form.

61. . The vertices of square ABCD are the midpoints of the sides of a larger square. Find the perimeter and the area of square ABCD. Round to the nearest hundredth.

62. Given with = 22, find the length of midsegment .

63. Find the two missing side lengths.

64. Find the two missing side lengths.

65. Find the missing side.

66. A painter leans a 15 foot ladder against a house. The base of the ladder is 5 feet from the house. To the nearest tenth of a foot, how high on the house does the ladder reach?

67. Find the length of each leg.

68. Find the missing side lengths.

5 3

3060

8

3060

4

5

45

12

3 2

45