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Geometry A Exam Review, Chapters 1-6

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Final Exam Review Name

___________________________Hr.____ Final Exam Information:

• The Final Exam consists of a Multiple-Choice Section and an Open-Response Section. • You may not use notes of any kind on the Final Exam. • This Exam Review is designed to help prepare you for the exam. • In addition to successfully completing the exam review, you will need to study your notes. • Being well-prepared for the exam is of utmost importance! • All seven parts of the Exam Review are required; each section is worth 5 homework points.

Chapter 1

For Questions 1-4, use the figure at the right. 1. What is another name for ? 2. What is another name for line g? 3. Name three noncollinear points. 4. Name three collinear points. For Questions 5 and 6, use the figure at the right. 5. Name three coplanar points. 6. Name the intersection of planes RSP and PTW.


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7. Classify the polygon as concave or convex and regular or irregular. a) b) 8. Use the number line to find the measure. a) JL b) KN 9. Suppose A, B, and C are collinear , AB = 4x, BC = 5x, and AB = 16.

a) Draw and label the figure. b) Find x. SAW! c) Find BC. SAW!

10. Suppose S is the midpoint of , RS = 4x – 5, and ST = 11 + 2x. a) Draw and label the figure. b) Find x. SAW!


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c) Find ST. SAW! 11. Suppose Q is the midpoint of , QR = 6 – 3x, and PR = 14x + 2. a) Draw and label a figure that satisfies the given information. b) Find x. SAW! c) Find PR. SAW! 12. Find the length of . SAW! 13. Find the distance between Z(-1, 3) and M(8, -7). SAW! 14. Find the coordinates of the midpoint of a segment having endpoints A(0, 0) and D(-2, -8). SAW!


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15. Find the coordinates of the midpoint of a segment having endpoints R(-10, 5) and S(8, 4). SAW!

Chapter 2

16. Underline the hypothesis and double-underline the conclusion of the following statement.

If you complete the review packet, then you will earn a 5% bonus on the exam. 17. Identify the hypothesis of the following statement.

You will move on to Geometry B if you pass Geometry A. 18. Write the statement in if-then form.

Vertical angles are congruent. 19. Write the statement in if-then form.

The product of two even integers, a and b, is an even integer. 20. Write the converse of the conditional statement. Determine whether the converse is true or false.

If it is false, find a counterexample.

If you have a dog, then you are a pet owner. 21. Write the converse of the conditional statement. Determine whether the converse is true or false.

If it is false, find a counterexample.

If you live in Texas, then you live in the United States.


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22. Complete the truth table.

p q ~p ~p q T T

T F

F T

F F

23. Complete the truth table.

p q ~q p ~q T T

T F

F T

F F

For Questions 24-26, find x and the measures of each numbered angle. SAW! 24. 25.

26.


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For Questions 27-29, draw and label a figure. Then, write an equation to answer the question. 27. If bisects , m FGK = (3v – 4)°, and m KGH = (2v + 7)°, find m FGK. SAW! 28. Suppose RST is a right angle and point U is in the interior of RST.

If m RSU = 3(w – 4)° and m UST = (6w + 3)°, find w. SAW! 29. If is in the interior of , m = 55°, m ABD = (7x – 2)°,

and m DBC = (3x + 7)°, find m ABD. SAW!

Chapter 3

30. Use the figure at the right. a) Identify a pair of vertical angles. b) Identify a pair of corresponding angles. c) Identify a pair of alternate interior angles.


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d) Identify a pair of alternate exterior angles. e) Identify a pair of consecutive interior angles.

f) Identify a pair of supplementary angles.

g) Identify a linear pair. For Questions 31 and 32, use the figure at the right. 31. Identify the plane parallel to plane VWT. 32. Name a segment skew to . For 33 and 34, use the figure at the right. 33. Which of the following could prove j // k? A. 1 5 C. 4 10 B. 2 4 D. 3 10 34. Which of the following could prove g // h? A. 9 10 C. 4 10 B. 1 5 D. 3 6


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Chapter 4

For Questions 35 and 36, draw and label a figure. Then, write an equation to answer the question. 35. Find a and the measure of each side of equilateral triangle MNO if MN = 5a, NO = 4a + 6,

and MO = 7a – 12. SAW! 36. Triangle TAC is an isosceles triangle with vertex angle A. If TA = 3b + 1, AC = 4b – 11,

and TC = 6b – 2, find b, TA, AC, and TC. SAW!

37. Using the figure below, find the measures of the numbered angles. SAW! 38. Name the postulate that could prove the two triangles are congruent (SSS, SAS, ASA, AAS).

80°

45°

75°

1 2

3 4


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If there is not enough information, write Not Possible.

a) b) c) d) 39. Identify the congruent triangles in the figure at the below right. Be sure to name the corresponding vertices in the correct order!

ABC _________ For Questions 40-42, write a two-column proof. 40. Given: W is the midpoint of

W is the midpoint of

Prove:

41. Given: bisects

Prove:

Statements Reasons 1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

6. 6.


2. 2.

3. 3.

4. 4.

5. 5.

6. 6.

X

Z Y

W

V


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42. Given: is isosceles with base

Prove:

Chapter 5

43. Name the shortest and longest segments in the figure at the right. Shortest:______ Longest:______ 44. Identify the largest angle in the triangle at the right. A. EFD C. FDE B. FED D. DEF 45. Determine whether the given measures can be the lengths of the sides of a triangle.


2. 2.

3. 3.

4. 4.

5. 5.


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a) 1, 1, 2 b) 0.3, 0.4, 0.5 c) 1, 3, 5 46. Find the range for the measure of the third side of a triangle given the measures of two sides. a) 6 and 10 b) 32 and 34 47. In the figure at the right, lines a, b, and c are perpendicular bisectors of and meet at A. a) Point A is the circumcenter. What does this tell you about AP, AR, and AQ? (See 5.1 notes.)

b) Find x. SAW! c) Find PA. SAW! 48. Suppose U is the centroid of .

a) Find the value of UC. SAW! b) Find the value of x. SAW! c) Find the value of UT. SAW!

d) Find the value of y. SAW!


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e) Find the value of AU. SAW!

f) Find the value of z. SAW! For Questions 49 and 50, what would you assume to begin an indirect proof? 49. If 7x + 1 < 3, then x < 2. 50. Given: 3x + 5 = 35 Prove: x 5

Chapter 6

51. Consider the figure at the right. a) State whether the two triangles are similar. b) Find x. SAW! 52. Consider the figure at the right. a) State whether the two triangles are similar. b) Find x. SAW! 53. The ratio of cats to dogs at an animal shelter is 4:5. If there are currently 85 dogs at the shelter, how many cats are there? 54. A car is 7.5 feet long and 4.2 feet wide. A scale model is built with a width of 3 inches. How long is

x


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the scale model? 55. Candy corn costs 31 cents per ounce. What is the cost of the candy corn per pound? 56. If BD = 15, AD = 10, and CE = 8, find EB. 57. Find x if

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