Geometry Parallel and Perpendicular Line Review

Name: ______________________ Class: _________________ Date: _________ ID: A

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Geometry: Chapter 3 Review

1. (1 point) What four segments are parallel to plane PNRQ?

2. (1 point) What four segments are perpendicular to plane JKPN?

Use the diagram to find the following.

3. (1 point) Identify a pair of alternate exterior angles.

4. (1 point) What are three pairs of corresponding angles?

Name: ______________________ ID: A

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5. (1 point) What is the relationship between ∠3 and ∠6?

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

6. (1 point) If ∠8 measures 119, what is the sum of the measures of ∠1 and ∠4?

Name: ______________________ ID: A

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7. (1 point) Line r is parallel to line t. Find m∠5. The diagram is not to scale.

8. (1 point) Which is a correct two-column proof?

Given: l Ä mProve: ∠p and ∠k are supplementary.

9. (1 point) Find m∠Q. The diagram is not to scale.

Name: ______________________ ID: A

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10. (1 point) Find m∠G. The diagram is not to scale.

11. (1 point) Find the value of x. The diagram is not to scale.

12. (1 point) Find the values of x and y. The diagram is not to scale.

Name: ______________________ ID: A

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13. (1 point) Give the missing reasons in this proof of the Alternate Interior Angles Theorem.

Given: l Ä nProve: ∠4 ≅ ∠6

Statements Reasons

1. l Ä n

2. ∠2 ≅ ∠6

3. ∠4 ≅ ∠2

4. ∠6 ≅ ∠4

1. Given

a. ?

b. ?

c. ?

14. (1 point) Write a two-column proof.

Given: ∠2 and ∠5 are supplementary.Prove: l Ä m

Name: ______________________ ID: A

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15. (1 point) Which lines are parallel if m∠3 = m∠6? Justify your answer.

16. (1 point) Find the value of x for which p is parallel to q, if m∠1 = 4x and m∠3 = 112.The diagram is not to scale.

17. (1 point) Find the value of x for which l is parallel to m . The diagram is not to scale.

18. (1 point) Find the value of x for which l is parallel to m . The diagram is not to scale.

Name: ______________________ ID: A

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19. (1 point) State the missing reasons in this proof.

Given: ∠1 ≅ ∠5Prove: p Ä r

Statements Reasons

1. ∠1 ≅ ∠5

2. ∠4 ≅ ∠1

3. ∠4 ≅ ∠5

4. p Ä r

Given

a.____

b.____

c.____

20. (1 point) Each sheet of metal on a roof is parallel to the rest of the sheets of metal. If the first sheet of metal is perpendicular to the top line of the roof, what can you conclude about the rest of sheets of metal? Justify your answer.

Name: ______________________ ID: A

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21. (1 point) A carpenter cut the top section of window frame with a 37º angle on each end. The side pieces each have a 50º angle cut at their top end, as shown. Will the side pieces of the frame be parallel? Explain. Diagram not to scale.

22. (1 point) In a plane, line k is parallel to line l and line k is parallel to line m . What can you conclude about the relationship between lines l and m?

23. (1 point) Find the value of k. The diagram is not to scale.

Name: ______________________ ID: A

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24. (1 point) Find the values of x, y, and z. The diagram is not to scale.



27. (1 point) A star patterned quilt has a star with the angles shown. What is the value of x? The diagram is not to scale.

Name: ______________________ ID: A

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28. (1 point) Find the measure of each interior and exterior angle. The diagram is not to scale.

29. (1 point) What is the slope of the line shown?


Name: ______________________ ID: A

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32. (1 point) Write the equation for the vertical line that contains point E(–7, 7).

33. (1 point) Write the equation for the horizontal line that contains point G(4, 8).

34. (1 point) Is the line through points P(8, 3) and Q(4, 2) parallel to the line through points R(–5, –5) and S(–1, –2)? Explain.

35. (1 point) Which two lines are parallel?I. 5y = −3x − 5II. 5y = −1 − 3xIII. 3y − 2x = −1

36. (1 point) Is the line through points P(1, 9) and Q(9, 6) perpendicular to the line through points R(–6, 0) and S(–9, 8)? Explain.

37. (1 point) What must be true about the slopes of two perpendicular lines, neither of which is vertical?

38. (1 point) Are the lines y = –x – 2 and 4x + 4y = 16 perpendicular? Explain.

ID: A

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Geometry: Chapter 3 ReviewAnswer Section

1. ANS: segments JK, KL, ML, and JM

PTS: 1 REF: 3-1 Lines and Angles 2. ANS:

segments JM, KL, PQ, and NR


∠2 and∠6


angles 1 & 7, 8 & 6, and 2 & 4


alternate interior angles


238

PTS: 1 REF: 3-2 Properties of Parallel Lines 7. ANS:

135


Statements R e asons

1. l Ä m 1. Given

2. ∠p ≅ ∠d 2. Vertical Angles

3. ∠d and ∠c are supplementary. 3. Same-Side Interior Angles

4. ∠c ≅ ∠k 4. Vertical Angles

5. ∠p and ∠k are supplementary. 5. Substitution

PTS: 1 REF: 3-2 Properties of Parallel Lines

ID: A

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9. ANS: 66


34º


11


x = 77, y = 57


a. Corresponding anglesb. Vertical anglesc. Transitive Property


[4]Statements Reasons

1. ∠2 and ∠5 are supplementary

2. ∠3 ≅ ∠2

3. ∠3 and ∠5 are supplementary

4. l Ä m

1. Given

2. Vertical angles

3. Substitution

4. Converse of Same-SideInterior Angles Theorem

[3] correct idea, some details inaccurate[2] correct idea, some statements missing[1] correct idea, several steps omitted


r Ä s, by the Converse of the Alternate Interior Angles Theorem

PTS: 1 REF: 3-3 Proving Lines Parallel 16. ANS:

28

PTS: 1 REF: 3-3 Proving Lines Parallel

ID: A

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17. ANS: 28


41


a. Vertical angles.b. Transitive Property.c. Alternate Interior Angles Converse.


The sheets of metal are all perpendicular to the top line of the roof by the Perpendicular Transversal Theorem.

PTS: 1 REF: 3-4 Parallel and Perpendicular Lines 21. ANS:

No. The angles for each corner form a 87º angle (37º + 50º). 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 90º.


Lines l and m are parallel. It is given that line k is parallel to line l and line k is parallel to line m Therefore, line l is parallel to m , because if two lines are parallel to the same line, then they are parallel to each other.


73

PTS: 1 REF: 3-5 Parallel Lines and Triangles 24. ANS:

x = 86, y = 75, z = 94


33


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PTS: 1 REF: 3-5 Parallel Lines and Triangles

ID: A

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27. ANS: 81


m∠1 = m∠2 = m∠3 = 90, m∠4 = 114, m∠5 = m∠6 = 66, m∠8 = 24, m∠7 = m∠9 = 156


− 139

PTS: 1 REF: 3-7 Equations of Lines in the Coordinate Plane 30. ANS:

513


− 18


x = –7


y = 8


No; the lines have unequal slopes.

PTS: 1 REF: 3-8 Slopes of Parallel and Perpendicular Lines 35. ANS:

I and II


No, their slopes are not opposite reciprocals.


The slopes have product –1.

PTS: 1 REF: 3-8 Slopes of Parallel and Perpendicular Lines

ID: A

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38. ANS: No; their slopes are not opposite reciprocals.

PTS: 1 REF: 3-8 Slopes of Parallel and Perpendicular Lines

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Geometry Parallel and Perpendicular Line Review