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8.G.5 [565782]StudentClassDate

1. In the figure below, what is the measure of ∠x?

A. 80°

B. 90°

C. 100°

D. 110°

2. Which expression is equivalent to the measure of in the image below?

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A.

B.

C.

D.

3.

Triangle JKL is shown below.

What is the measure of angle KJL?

A. 15°

B. 20°

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C. 35°

D. 60°

4. Joey and Emily’s teacher gave them each a triangle divided into three parts—A, B, and C—which looked like the triangle shown below. They were told to cut the pieces apart and rearrange them into a figure that will prove that the sum of the interior angles of a triangle is always equal to 180°.

Joey’s and Emily’s figures are shown below.

Who has created the correct figure and why?

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A. Joey, because the interior angles of the original triangle form a straight line

B. Emily, because all of the vertices of the original triangle are touching

C. Joey, because the cut edges all face the same way

D. Emily, because the cut edges form a circular figure

5. Consider the diagram and angle measures shown below.

What is the value of

A.

B.

C.

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D.

6. In the diagram, line l is parallel to line m.

Explained in one step, why is

A. If lines are parallel, corresponding angles are congruent.

B. If lines are parallel, alternate interior angles are congruent.

C. If lines are parallel, alternate exterior angles are congruent.

D. If lines are parallel, same-side interior angles are congruent.

7. In the figure below, lines l and k are parallel.

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Which statement(s) can be used to prove that Angle 1 is congruent to Angle 3?

A. Angle 1 and Angle 3 are congruent because they both measure more than 90°.

B. Angle 1 and Angle 3 are congruent because they each have a sum of 180° when added to the measure of Angle 2.

C. Angle 1 and Angle 2 are congruent because corresponding angles of parallel lines cut by a transversal are congruent.Angle 1 and Angle 3 are congruent because corresponding angles of parallel lines cut by a transversal are congruent.

D. Angle 2 and Angle 3 are congruent because vertical angles are congruent.Angle 1 and Angle 2 are congruent because corresponding angles of parallel lines cut by a transversal are congruent.Angle 1 and Angle 3 are congruent because they are both congruent to Angle 2.

8. In the figure below, lines m and n are parallel, with

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Which statement correctly describes how to find the measure of

A. Since are alternate interior angles, the measure of is also 62°. The measures of must add up to 180°. Since

the measure of must be 45°.

B. Since are corresponding angles, the measure of is also 62°. The measures of must add up to 180°. Since


C. Since are vertical angles, the measure of is also 73°. Since are alternate interior angles, the measure of is also 73°. The measures of must add up to Since


D. The measures of must add up to 180°. Since the measure of must be 45°. Since are

alternate interior angles, the measure of is also 45°. The measures of must add up to 180°. Since the measure of must be 62°.

9. In the figure below, line segment MN is parallel to line OP.

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Which of these best describes the measure of angle c?

A. The measure of angle c is 36° because angle b and angle c are vertical angles.

B. The measure of angle c is 144° because of the properties of the exterior angles of a triangle.

C. The measure of angle c is 44° because line segment NO is a transveral and angles N and b are corresponding angles.

D. The measure of angle c is 100° because line segment MO is a transversal and angles m and c are alternate interior angles.

10. In the image below, the measure of angle 3 is equal to the sum of the measures of angle 6 and what other angle?

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11. In the figure below, lines j and k are parallel.

What is the measure of ∠x?

A. 24°

B. 33°

C. 57°

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D. 66°

12. Right triangle JKL is shown below.

What is the measure of ∠KLM?

A. 120°

B. 126°

C. 135°

D. 144°

13. In the figure below, lines m and n are parallel.

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What is the measure of angle y?

A. 25°

B. 36°

C. 55°

D. 88°

14. In the figure below, lines e and f are parallel.

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What is the measure of ∠w?

A. 45°

B. 50°

C. 65°

D. 70°

15. Three rays intersect to form the triangle shown.

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Part A What is the sum, in degrees, of and ?

Part B Justify your answer to Part A by giving an informal argument using three facts about the angles shown in the diagram.

16. The figure below shows triangle XYZ and its external angles.

Part A. What is the sum of the measures of x, y, and z? Explain how you know using words and/or equations.

Part B. Find the measures of the three angles marked in the figure below.

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Use words, numbers, and/or pictures to show your work.

17. Triangle PQR is shown below.

What is the measure of ∠QRS?

A. 76°

B. 104°

C. 118°

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D. 138°


What is the measure of ∠x?

A. 40°

B. 35°

C. 20°

D. 15°

19. Triangle EFG is shown below.

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What is the measure of ∠EFG?

A. 52°

B. 85°

C. 90°

D. 137°

20. The diagram shows two parallel lines cut by a transversal line segment.

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Which relationship is true?

A.

B.

C.

D.

21. Triangle PQR is shown below.

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What is the value of x?

A. 12

B. 13

C. 25

D. 40

22. In the figure below, lines f and g are parallel.

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What is the measure of ∠z?

A. 74°

B. 106°

C. 136°

D. 150°

23. In the diagram below,

If line e is parallel to line m, which set of congruence statements explains why

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A.

B.

C.

D.

24. What is the value of x in the figure below?

A. 80

B. 90

C. 100

25. What is the value of x in the figure below?

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A. 17

B. 23

C. 24

D. 36

26. The diagram below shows some of the angles formed by three streets on a map.

Which of the following shows both a correct angle measure and a property that justifies the angle measure?

A. based on the definition of vertical angles

B. based on the sum of interior angles of a triangle

C. based on the definition of right angles

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D. based on the definition of supplementary angles

27. Lines v and w are parallel.


A. 6

B. 8

C. 30

D. 39

28. In the figure below, lines e and f are parallel.

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What is the measure of angle x?

A. 30°

B. 40°

C. 50°

29. Triangle PQR is shown in the diagram.

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Which equation must be true?

A.

B.

C.

D.

30. Sarah drew a triangle. She claimed that if there were another triangle with two angles congruent to two of the angles in her original triangle, the two triangles would be similar. Kristin drew a triangle to determine if Sarah’s statement was true.

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Which statement best explains the relationship between Sarah’s triangle and Kristen’s triangle?

A. Kristin’s triangle should be larger than Sarah’s triangle since 60° > 50°.

B. Kristin’s triangle appears to be similar to Sarah’s triangle but does not have the two congruent angles.

C. Kristin’s triangle needs an angle smaller than 50˚ since her triangle is smaller than Sarah’s triangle.

D. Kristin’s triangle has two congruent angles to Sarah’s triangle and is similar to Sarah’s triangle.

31. Triangle JKL is shown below.

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What is the measure of ∠KLM?

A. 135°

B. 115°

C. 110°

32. In the figure below, lines x and y are parallel.

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What is the value of n?

A. 10

B. 26

C. 36



A. 34

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B. 58

C. 63

D. 75

34. In the figure below, lines e and f are parallel. Line g is perpendicular to line e.

What is the measure of angle w?

A. 32°

B. 45°

C. 52°

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D. 58°

35. Triangle MNP is shown below.

What is the measure of ∠NPR?

A. 115°

B. 125°

C. 130°

D. 140°

36. Lines e and f are parallel.

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What is the measure of ∠g?

A. 48°

B. 53°

C. 79°

D. 90°

37. Triangle FGH is shown below.

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What is the measure of ∠FGH?

A. 22°

B. 23°

C. 44°

D. 46°

38. The figure below shows ray DE intersecting parallel lines and .

Based on the figure, what is the rule that supports the fact that

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39. Geometry Demonstrations

A square corner makes a angle (right angle). Use this fact to make discoveries about angles and triangles.

Part A. Each of the angles of this rectangle measures

A diagonal line cuts each of the opposite angles into two smaller angles.

Cut a rectangular piece of paper in two along the diagonal. Rotate the pieces to show that the diagonal line forms two congruent triangles.

Use these facts to show that the sum of the angles of the right triangle is

Part B. The diagonal line forms a transversal that cuts the parallel sides of the rectangle.

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Identify at least three pairs of congruent angles in the figure. Explain their relationship using the proper terms and names.

Part C. Angle h is an exterior angle of the dotted triangle. What is the relationship of angle h to the angles of the dotted triangle? How do you know?

Part D. The triangle below is not a right triangle. The perpendicular line divides the triangle into two right triangles. Show that the sum of the angle measures of this non-right triangle is

Use words, numbers, and/or pictures to show your work.

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40. Triangle NPQ is shown below.

What is the measure of ∠NQP?

A. 22°

B. 23°

C. 24°

D. 26°

41. Triangle QRS is shown below.

What is measure of angle QRS?

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A. 110°

B. 135°

C. 155°

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