Name: ________________________ Class: ___________________ Date: __________

ID: A

Geometry - Chapter 3 Test REVIEW 3. Find m∠G. p Ä r. The diagram is not to scale.

1. Which angles are corresponding angles?

A. B. C. D.

∠7 and ∠3 ∠8 and ∠3 ∠3 and ∠11 none of these

2. Which statement is true? A. B. C. D.

A. B. C. D.

34 110 104 146

4. In a plane, line k is parallel to line l and line j is perpendicular to line l. What can you conclude about the relationship between lines j and k?

∠FEG and ∠CBE are alternate angles. ∠CBE and ∠DEB are alternate angles. ∠CBE and ∠DEB are same-side interior angles. ∠FEG and ∠DEB are same-side interior angles.

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Name: ________________________

ID: A 8. Find the value of x for which l is parallel to m. The diagram is not to scale.

This diagram of airport runway intersections shows two parallel runways. A taxiway crosses both runways.

A. B. C. D.

100 80 123 41

9. Find the values of x, y, and z. The diagram is not to scale.

5. How are ∠8 and ∠4 related? A. alternate interior angles B. corresponding angles C. same-side interior angles D. none of these

A. B. C. D.

6. If ∠8 measures 127, what is the sum of the measures of ∠1 and ∠4? A. 254 B. 307 C. 127 D. 106

x x x x

= = = =

y y y y

= = = =

74, z = 106 106, z = 74 106, z = 62 62, z = 106

10. Find the value of x for which p is parallel to q, if m∠1 = (9x) and m∠3 = 117.The diagram is not to scale.

7. Find m∠P. The diagram is not to scale.

A. B. C. D. A. B. C. D.

62, 62, 74, 74,

106 74 64 84

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108 13 117 126

Name: ________________________

ID: A 14. Which lines are parallel if m∠2 = m∠8? Justify your answer.

11. Find the value of x. The diagram is not to scale.

A. B. C. D.

11 34 21 67

A. r Ä s, by the Converse of the Alternate Interior Angles Theorem B. r Ä s, by the Converse of the Same-Side Interior Angles Postulate C. l Ä m, by the Converse of the Same-Side Interior Angles Postulate D. l Ä m, by the Converse of the Alternate Interior Angles Theorem

12. The expressions in the figure below represent the measures of two angles. Find the value of x. f Ä g . The diagram is not to scale.

15. Find the value of k. The diagram is not to scale.

A. B. C. D.

13 12 –12 11

13. The folding chair has different settings that change the angles formed by its parts. Suppose m∠2 is 34 and m∠3 is 76. Find m∠1. The diagram is not to scale.

A. B. C. D.

A. B. C. D.

130 110 100 120

3

100 80 103 54

Name: ________________________

ID: A 18. What is the slope of the line shown?

16. Find the value of x. The diagram is not to scale. Given: ∠SRT ≅ ∠STR, m∠SRT = 28, m∠STU = 2x

A. B. C. D.

28 30 14 76

A. − B. C.

17. A star patterned quilt has a star with the angles shown. What is the value of x? The diagram is not to scale.

7 9

9 7 7 9

D. −

9 7

2 19. What is the graph of y = − x – 3? 3 A.

A. B. C. D.

99 91 81 105

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Name: ________________________

ID: A

B.

A.

C.

B.

D. C.

20. What is the graph of 5x − 2y = −10?

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Name: ________________________

ID: A C.

D.

D. 21. What is the graph of y − (−6) = 2 / 3(x − (−5)) ? A.

22. Write an equation in point-slope form of the line through point J(8, 7) with slope 5. A. y − 7 = 5(x + 8) B. y + 7 = 5(x + 8 ) C. y − 7 = −5 (x − 8 ) D. y − 7 = 5(x − 8)

B.

23. Write an equation in slope-intercept form of the line through points S(–1,–2) and T(6,8). 4 10 A. y = − x + 7 7 10 4 B. y = x + 7 7 10 4 C. y = − x – 7 7 10 4 D. y = x – 7 7

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Name: ________________________

ID: A

24. What is an equation for the line that passes through points (7, –9) and (6, 2)? A. (y – 9) = 11(x + 7) B. (y + 9) = 11(x – 7) C. (y – 9) = –11(x + 7) D. (y + 9) = –11(x – 7)

26. Write the equation for the vertical line that contains point E(–7, 7). A. y = 7 B. x = –7 C. y = –7 D. x = 7

25. What is an equation in slope-intercept form for the line given?

27. Write the equation for the horizontal line that contains point G(3, 4). A. x = 4 B. y = 4 C. y = 3 D. x = 3

A. B. C. D.

y = 1 / 3(x) + (−2 / 3) y = 3(x) + (−10 / 3) y = 3(x) + (−2 / 3) y = 1 / 3(x) − (−4)

28. Is the line through points P(3, 2) and Q(–1, –4) parallel to the line through points R(1, 1) and S(–5, 0)? Explain. A. No; the lines have unequal slopes. B. No; one line has zero slope, the other has no slope. C. Yes; the lines have equal slopes. D. Yes; the lines are both vertical. 29. What is the equation in point-slope form for the line parallel to y = 4x – 8 that contains P(–2, –7)? A. y + 7 = 4(x + 2) C. y – 7 = 4(x + 2) B. x + 7 = –4(y + 2) D. y + 7 = –4(x + 2) 30. Is the line through points P(4, 4) and Q(1, 9) perpendicular to the line through points R(3, –1) and S(8, –4)? Explain. A. Yes; their slopes have product –1. B. No, their slopes are not opposite reciprocals. C. Yes; their slopes are equal. D. No; their slopes are not equal.

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Name: ________________________

ID: A

31. What must be true about the slopes of two perpendicular lines, neither of which is vertical? A. The slopes are equal. B. The slopes have product 1. C. The slopes have product –1. D. One of the slopes must be 0.

32. What is an equation in point-slope form for the line perpendicular to y = 5x – 14 that contains (–10, –6)? A. y + 6 = 5(x + 10) 1 B. y + 6 = − (x + 10) 5 1 C. y + 10 = − (x + 6) 5 D. x + 6 = 5(y + 10)

33. Are the lines y = –x – 1 and 5x + 5y = 15 perpendicular? Explain. A. No; their slopes are not opposite reciprocals. B. Yes; their slopes are equal. C. No; their slopes are not equal D. Yes; their slopes have product –1. 34. Find the values of the variables. Show your work and explain your steps. The diagram is not to scale.

35. A carpenter cut the top section of window frame with a 42° angle on each end. The side pieces each have a 47° angle cut at their top end, as shown. Will the side pieces of the frame be parallel? Explain. Diagram not to scale.

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ID: A

Geometry - Chapter 3 Test REVIEW Answer Section 1. 2. 3. 4.

5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.

C C A Lines j and k are perpendicular. It is given that line k is parallel to line l and line j is perpendicular to line l Therefore, line j is perpendicular to k, because in a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other. B A B D D B A B B D B D C B A C C D D D A B B A A B C B A

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ID: A 34. [4]

Because the three interior angles of a triangle have measures with sum 180, w + 31 + 90 = 180, so w = 59°. Because vertical angles are congruent, y = 59°. Because supplementary angles have measures with sum 180, x = v = 121°. Because the three interior angles of a triangle have measures with sum 180, z + 68 + y = z + 68 + 59 = 180, so z = 53°. [3] small error leading to one incorrect answer [2] three correct answers, work shown [1] two correct answers, work shown 35. No. The angles for each corner form a 89° angle (42° + 47°). In order for the side pieces to be parallel, the sum of the angle of the top piece and the angle of the side piece must be exactly 90°.

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