Int. Geometry Unit 3 Test Review 1

60°

70°

5

4 3

2 1

98

76

Directions 1-6: Fill in the missing word with sometimes, always, or never to complete the statement

1. Two lines perpendicular to the same line are __________________skew. 2. Through a point outside a line, there is _______________ exactly one line

parallel to the given line. 3. Two lines parallel to a third line are ______________ perpendicular to each other. 4. The acute angles of an obtuse triangle are ___________________ complementary. 5. If two lines are cut by a transversal, then alternate interior angles are

___________ congruent. 6. The exterior angle of a triangle is _____________ equal to the sum of the remote

interior angles Directions 7-11: Use the diagram to find the measure of the following angles. 7. 1 _?_m∠ = 8. 2 _?_m∠ = 9. 3 _?_m∠ = 10. 4 _?_m∠ = 11. 5 _?_m∠ = Directions 12-14: Use the diagram and the given information to find the value of x WARNING: EACH PROBLEM BELOW IS A SEPARATE PROBLEM 12. 6 ; 8 20m x m x∠ = ∠ = −

Int. Geometry Unit 3 Test Review 2

a

b

c d

181716 15

141312 11

10

9 876

54321

98

76

13. 7 ; 9 3 20m x m x∠ = ∠ = + 14. 8 3 8 ; 9 2 10m x m x∠ = − ∠ = + Directions 15-19: Write the letter of the choice that best completes each statement. Use

the figure below. (A) 𝑎 ∥ 𝑏 (B) 𝑐 ∥ 𝑑 (C) 𝑎 ∥ 𝑏 and 𝑐 ∥ 𝑑 (D) no conclusion 15. If 3 13∠ ≅ ∠ , then _________ 16. If 7 18∠ ≅ ∠ , then _________ 17. If 5 and 8 are supplementary∠ ∠ , then _________ 18. If 16 10∠ ≅ ∠ , then _________ 19. If 8 and 10 are supplementary∠ ∠ , then _________ 20. The exterior angles of a triangle are in the ratio of 2:3:4. What are the (interior)

angles of the triangle?

Int. Geometry Unit 3 Test Review 3

x+y

2y

x

B

E

D

A

C

50°

w

85°

45°

A

B

C

D

E

F

4x - 10

x + 10x

B A

D

E F

C

21. Is it possible for the angles in the diagram to have the measures indicated? Why or why not?

22. Find the value of w. 23. Is it possible for two exterior angles of a triangle to be supplementary? Why or

why not? 24. Find the value of x.

Int. Geometry Unit 3 Test Review 4

c

d

a b

1211109

87654321

F

A

D E

B C

G

4 3

21

A

B ED

C

c

d

a b

1211109

87654321

25. The three angles of a triangle have measures 2 , 3 5m A x y m B x y∠ = − ∠ = + , and 5 3m C x y∠ = − . Find x.

Directions 26-29: Proofs – make marks on the drawings to help you. 26. Given: 𝑎 ∥ 𝑏 and 𝑚∠2 ≠ 𝑚∠10 Prove: is not parallel to c d

27. Given: 𝑎 ∥ 𝑏; ∠8 ≅ ∠12 Prove: 𝑐 ∥ 𝑑 28. Given: 𝐴𝐵 ∥ 𝐶𝐷; ∠1 ≅ ∠4 Prove: DA bisects BDC∠

29. Given: ; AG BC AG DE⊥ ⊥ Prove: ACF CED∠ ≅ ∠

Int. Geometry Unit 3 Test Review 5

17

7

15

8 2

8

8

88

8

F

A

D

B

C E

65

4321

Directions 30-35: Write the letter of the name that best describes each triangle. (A) Scalene acute triangle (E) Isosceles right triangle (B) Scalene right triangle (F) Isosceles obtuse triangle (C) Scalene obtuse triangle (G) Equilateral triangle (D) Isosceles acute triangle 30. ABCΔ 31. BCDΔ 32. BDEΔ 33. BCEΔ 34. CEFΔ 35. ACFΔ Questions 36-40: Use the given information and the diagram to find the indicated value. 36. If 2 30m∠ = and 6 80m∠ = , find 3m∠ . 37. If 1 160m∠ = and 3 70m∠ = , find 6m∠ . 38. If 4 110m∠ = and 5 100m∠ = , find 1m∠ . 39. If 2 40m∠ = and 3 6m m∠ = ∠ , find 3m∠ . 40. If 6 90m∠ = , find 1 4m m∠ + ∠ .

Int. Geometry Unit 3 Test Review 6

24°100°

4y°

5x°

45°

Questions 41-42: Find the indicated value based of the diagram. 41. Find the value of x 42. Find the value of y. Selected Answers: 1. sometimes 2. always 3. never 4. never 5. sometimes 6. always 7. 60 8. 50 9. 50 10. 90 11. 40 12. 55x = 13. 40x = 14. 178

5x =

15. A 16. D 17. B 18. B 19. A 20. 20 ,60 ,100 21. No, answers will vary 22. 90w = 23. No, answers will vary 24. 30x = 25. 20x = Note with the proofs, there are multiple solutions to these problems.

26. Temp. assume 𝑐 ∥ 𝑑 and we are given 𝑎 ∥ 𝑏 so we know corresponding angles are congruent with parallel lines, giving 2 4m m∠ = ∠ and 10 4m m∠ = ∠ .

Using substitution 10 2m m∠ = ∠ , which contradicts the given information 2 10m m∠ ≠ ∠ . This means our assumption is false and c is not parallel to

d 27.

Statement Reason Relies on 1. 𝑎 ∥ 𝑏 1. Given 2. 6 8∠ ≅ ∠ 2. Corresponding angles are congruent 1 3. 12 8∠ ≅ ∠ 3. Given 4. 6 12∠ ≅ ∠ 4. Transitive property 2 and 3 5. 𝑐 ∥ 𝑑 5. Corresponding angles are congruent 4

Int. Geometry Unit 3 Test Review 7

28.

29.

30. G 31. E 32. C 33. B 34. D 35. F 36. 70 37. 90 38. 150 39. 70 40. 270 41. 11x = 42. 14y =

Statement Reason Relies on 1. 𝐴𝐵 ∥ 𝐶𝐷 1. Given 2. 4 2∠ ≅ ∠ 2. Alternate Interior Angle Theorem 1 3. 4 1∠ ≅ ∠ 3. Given 4. 2 1∠ ≅ ∠ 4. Transitive property 2 and 3 5. DA bisects BDC∠

5. Definition of an angle bisector 4

Statement Reason Relies on

1. ; AG BC AG DE⊥ ⊥ 1. Given

2. 𝐵𝐶 ∥ 𝐷𝐸 2. Two lines in a plane perpendicular to the same line are parallel

1

3. ACF CED∠ ≅ ∠ 3. Corresponding angles must be congruent

2