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GEOM CH. 3.1.-3.5 REVIEW
[pic]
____ 1. What four segments are parallel to plane MRQL?
|A. |segments JK, KL, JM, and ML|C. |segments JK, JN, NP, and KP|
|B. |segments NP, KP, PQ, and JN|D. |segments JM, KL, NR, and PQ|
Use the diagram to find the following.
[pic]
____ 2. Identify a pair of alternate exterior angles.
|A. |[pic] |C. |[pic] |
|B. |[pic] |D. |[pic] |
____ 3. Which angles are corresponding angles?
[pic]
|A. |[pic] |C. |[pic] |
|B. |[pic] |D. |none of these |
____ 4. Which statement is true?
[pic]
|A. |[pic]are alternate angles. |
|B. |[pic]are alternate angles. |
|C. |[pic]are same-side interior angles. |
|D. |[pic]are same-side interior angles. |
____ 5. Which is a correct two-column proof?
Given: [pic]
Prove: [pic] and [pic] are supplementary.
[pic]
|A. | |
| |[pic] |
|B. | |
| |[pic] |
|C. | |
| |[pic] |
|D. |none of these |
____ 6. Find [pic] The diagram is not to scale.
[pic]
|A. |66 |B. |56 |C. |124 |D. |103 |
____ 7. Find [pic] The diagram is not to scale.
[pic]
|A. |106 |B. |74 |C. |64 |D. |84 |
____ 8. Find the value of x. [pic]. The diagram is not to scale.
[pic]
|A. |148 |B. |116 |C. |64 |D. |32 |
____ 9. Which lines are parallel if [pic]? Justify your answer.
[pic]
|A. |[pic], by the Converse of the Same-Side Interior Angles |
| |Postulate |
|B. |[pic], by the Converse of the Alternate Interior Angles |
| |Theorem |
|C. |[pic], by the Converse of the Alternate Interior Angles |
| |Theorem |
|D. |[pic], by the Converse of the Same-Side Interior Angles |
| |Postulate |
____ 10. Find the value of x for which p is parallel to q, if [pic].The diagram is not to scale.
[pic]
|A. |108 |B. |13 |C. |117 |D. |126 |
____ 11. Find the value of x for which l is parallel to m. The diagram is not to scale.
[pic]
|A. |100 |B. |80 |C. |123 |D. |41 |
____ 12. Each sheet of metal on a roof is perpendicular to the top line of the roof. What can you conclude about the relationship between the sheets of roofing? Justify your answer.
[pic]
|A. |The sheets of metal are all parallel to each other by the |
| |Transitive Property of Parallel Lines. |
|B. |The sheets of metal are all parallel to each other by the |
| |Alternate Interior Angles Theorem. |
|C. |The sheets of metal are all parallel to each other because |
| |in a plane, if a line is perpendicular to one of two |
| |parallel lines, then it is also perpendicular to the other. |
|D. |The sheets of metal are all parallel to each other because |
| |in a plane, if two lines are perpendicular to the same line,|
| |then they are parallel to each other. |
____
13. Find the value of k. The diagram is not to scale.
[pic]
|A. |72 |B. |108 |C. |105 |D. |42 |
____ 14. Find the value of x. The diagram is not to scale.
[pic]
|A. |33 |B. |162 |C. |147 |D. |75 |
____ 15. Find the value of x. The diagram is not to scale.
[pic]
|A. |33 |B. |70 |C. |23 |D. |13 |
____ 16. The folding chair has different settings that change the angles formed by its parts. Suppose [pic] is 34 and [pic] is 76. Find [pic]. The diagram is not to scale.
[pic]
|A. |130 |B. |110 |C. |100 |D. |120 |
____ 17. NO QUESTION
____ 18. NO QUESTION
____ 19. What is the slope of the line shown?
[pic]
|A. |[pic] |C. |[pic] |
|B. |[pic] |D. |[pic] |
____ 20. What is the graph of y = [pic]x – 2?
|A. |[pic] |C. |[pic] |
|B. |[pic] |D. |[pic] |
____
21. What is the graph of [pic]?
|A. |[pic] |C. |[pic] |
|B. |[pic] |D. |[pic] |
____ 22. Write an equation in point-slope form of the line through point J(4, –4) with slope 4.
|A. |[pic] |C. |[pic] |
|B. |[pic] |D. |[pic] |
____ 23. What is an equation for the line that passes through points (4, –4) and (8, 4)?
|A. |(y – 4) = 2(x + 4) |C. |(y – 4) = –2(x + 4) |
|B. |(y + 4) = 2(x – 4) |D. |(y + 4) = –2(x – 4) |
____ 24. Is the line through points P(3, –5) and Q(1, 4) parallel to the line through points R(–1, 1) and S(3, –3)? Explain.
|A. |Yes; the lines have equal slopes. |
|B. |No; the lines have unequal slopes. |
|C. |No; one line has zero slope, the other has no slope. |
|D. |Yes; the lines are both vertical. |
____ 25. What is the equation in point-slope form for the line parallel to y = 5x – 4 that contains P(–6, 1)?
|A. |x – 1 = –5(y + 6) |C. |y – 1 = –5(x + 6) |
|B. |y + 1 = 5(x + 6) |D. |y – 1 = 5(x + 6) |
____ 26. Is the line through points P(–3, –2) and Q(2, 3) perpendicular to the line through points R(10, –1) and S(15, –6)? Explain.
|A. |No, their slopes are not opposite reciprocals. |
|B. |No; their slopes are not equal. |
|C. |Yes; their slopes have product –1. |
|D. |Yes; their slopes are equal. |
____ 27. What is an equation in point-slope form for the line perpendicular to y = 2x + 13 that contains (8, –4)?
|A. |y + 4 = [pic](x – 8) |C. |y + 4 = 2(x – 8) |
|B. |x + 4 = 2(y – 8) |D. |y + 8 = [pic](x – 4) |
____ 28. Give the slope-intercept form of the equation of the line that is perpendicular to
–7x – 8y = 12 and contains P(–3, 1).
|A. |y – 3 = [pic](x + 1) |C. |y = [pic]x + [pic] |
|B. |y = [pic]x [pic] |D. |y – 1 = [pic](x + 3) |
29. Give the missing reasons in this proof of the Alternate Interior Angles Theorem.
Given: [pic]
Prove: [pic]
[pic]
[pic]
30. The 8 rowers in the racing boat stroke so that the angles formed by their oars with the side of the boat all stay equal. Explain why their oars on either side of the boat remain parallel.
31. Find the measure of each interior and exterior angle. The diagram is not to scale.
[pic]
32. Identify the form of the equation –3x – y = –2. To graph the equation, would you use the given form or change to another form? Explain.
33. Write a two-column proof.
Given: [pic] are supplementary.
Prove: [pic]
[pic]
34. Find the values of the variables. Show your work and explain your steps. The diagram is not to scale.
[pic]
35. 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?
[pic]
36. Line p contains points A(–7, –9) and B(4, 0). Line q is parallel to line p. Line r is perpendicular to line q. What is the slope of line r? Explain.
GEOM CH. 3.1.-3.5 REVIEW
Answer Section
1. ANS: C
2. ANS: A
3. ANS: C
4. ANS: C
5. ANS: A
6. ANS: B
7. ANS: B
8. ANS: D
9. ANS: A
10. ANS: B
11. ANS: D
12. ANS: D
13. ANS: A
14. ANS: A
15. ANS: D
16. ANS: B
17. ANS: A
18. ANS: C
19. ANS: B
20. ANS: B
21. ANS: C
22. ANS: B
23. ANS: B
24. ANS: B
25. ANS: D
26. ANS: C
27. ANS: A
28. ANS: C
29. ANS:
a. Corresponding angles
b. Vertical angles
c. Transitive Property
30. ANS:
The rowers keep corresponding angles congruent.
31. ANS:
[pic]
32. ANS:
Standard form. Answer may vary. Sample: You could use the given form. Find the intercepts and use them to draw the line.
33. ANS:
|[4] |[pic] |
|[3] |correct idea, some details inaccurate |
|[2] |correct idea, some statements missing |
|[1] |correct idea, several steps omitted |
PTS: 1
34. ANS:
|[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. ANS:
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.
36. ANS:
[pic]; Line r is perpendicular to line p because a line perpendicular to one of two parallel lines is also perpendicular to the other. Thus, the slope of line r is the opposite reciprocal of the slope of line p.
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