georgia performance 7a parallel and perpendicular lines · parallel lines perpendicular lines...

ex plo rat i o n

Parallel and Perpendicular Lines

7A

A carpenter cuts boards at different angles.

The board below is cut at a 45° angle.

Copyright © by Holt, Rinehart and Winston. 190 Holt MathematicsAll rights reserved.

45°

1. Label the angles formed by the cut.

2. Which angles are congruent, or have the same measure?

3. Which angles are supplementary, or have measures thatadd to 180°?

The board below is cut at a 30° angle.

4. Label the angles formed by the cut.

5. Which angles are congruent?

6. Which angles are supplementary?

Think and Discuss

7. Describe the top and bottom edges of the boards above.What kinds of lines do they form?

8. Describe the angles formed after cutting the board at a 90° angle.

30°

Georgia Performance

Standards

M8G1.a, M8G1.b


Parallel lines are lines in the same plane that never cross. When two parallel lines are intersected by a third line, the angles formed have specialrelationships. This third line is called a transversal.

In San Francisco, California, many streets are parallel such as Lombard St. and Broadway.

Columbus Ave. is a transversal that runs diagonal across them. The eight angles thatare formed are labeled on the diagram below.

Activity

1. Measure angles 1-8 in the diagram above. Write these measures in your table.

2. Use the table you completed and the corresponding diagram forthe following problems.

a. Angles inside the parallel lines are interior angles. Name them.

b. Angles outside the parallel lines are exterior angles. Name them.

c. Angles 3 and 6 and angles 4 and 5 are alternate interior angles. What do you notice about angles 3 and 6? What do younotice about angles 4 and 5?

d. Angles 2 and 7 and angles 1 and 8 are alternate exterior angles. Howdo the measures of each pair of alternate exterior angles compare?

Angle Number Angle Measure

1

2

3

4

5

6

7

8

Hands-On Lab 1Explore Parallel Lines and Transversals7A

LESSON

Name Date Class

1 23 4

5 67 8

Lombard st.

Broadway

Columbus ave.

e. Angles 1 and 5 are corresponding angles because they are inthe same position on each of the parallel lines. How do themeasures to angles 1 and 5 compare? Name another set ofcorresponding angles.

f. Add the measures of angles 1 and 2. Now add the measures ofangles 3 and 8. What can you say about the relationship of theangles in each of these sets. Name two other angles that havethe same relationship.

Think and Discuss

1. FG�� and LO�� are parallel. Tell what you know about the angles that are labeled 1 through 8.

2. If angle 2 measures 125, what are the measures of angles 1, 3, 4, 5, 6, 7, and 8?

3. If a transversal intersects two parallel lines and one of theangles formed measures 90°, discuss the relationship betweenall the angles.

Try This

Use a protractor to measure one angle in each diagram. Then findthe measures of all the other angles without using a protractor. Tellhow to find each angle measure.

1 23 4

5 67 8

1 23 4

5 67 8

6 85 7

2

LF

41 3

OG


Name Date Class

Hands-On Lab 1Explore Parallel Lines and Transversals (continued)7A

LESSON

Copyright © by Holt, Rinehart and Winston. 193 Holt Mathematics All rights reserved.

Activity

1. Parallel lines are two lines in a plane that never meet.Perpendicular lines intersect at 90� angles.

Prove the two lines below are parallel by measuring using atransversal and a protractor.

How did you prove the lines are parallel?

2. Prove that these lines are perpendicular using a protractor. Thenexplain your proof.

Hands-On Lab 2Parallel and Perpendicular Lines7A

LESSON

Name Date Class

Copyright © by Holt, Rinehart and Winston. 194 Holt Mathematics All rights reserved.

Think and Discuss

1. If an angle measured 38� in a line intersecting 2 parallel lines, how manyother angles would you expect to be 38� angles?

2. If a transversal intersects 2 parallel lines and you know one angle is 72�,why do you know every other angle?

Try ThisIn the space below, draw a set of parallel lines and a set of perpendicular lines.Draw a transversal intersecting the parallel lines. Measure and label the anglesthat prove that one set of lines is parallel and one set is perpendicular.

Hands-On LabParallel and Perpendicular Lines (continued)7A

LESSON

Name Date Class

Parallel Lines

Perpendicular Lines


Name Date Class

Parallel Lines Perpendicular Lines

Parallel lines never meet. Perpendicular lines form right angles.

When parallel lines are cut by a transversal,8 angles are formed, 4 acute and 4 obtuse.

The acute angles are all congruent.

The obtuse angles are all congruent.

Any acute angle is supplementary toany obtuse angle.

In each diagram, parallel lines are cut by a transversal. Namethe angles that are congruent to the indicated angle.

1. 2. 3.

The angles congruent The angles congruent The angles congruent to �1 are: to �a are: to �z are:

In each diagram, parallel lines are cut by a transversal andthe measure of one angle is given. Write the measures ofthe remaining angles on the diagram.

4. 5. 6.

135°

150°

150°

r sv txz

w y

bcd

afeh

g

2

68

41

57

3

60°

60°60°

60°120°

120°120°

120°

90°

25°

Review for MasteryParallel and Perpendicular Lines7A

LESSON


Name Date Class

1. Measure the angles formed by the transversal and the parallel lines. Which angles seem to be congruent.

In the figure, line x || line y. Find the measure of each indicatedangle, if the m � 8 � 34�.

2. �2 3. �3 4. �4

5. �6 6. �7 7. �1

In the figure, line m || line n. Find the measure of each angle,if m � 1 � 131�.

8. �2 9. �3 10. �4

11. �5 12. �6 13. �7

In the figure, line a || line b.

14. Name all angles congruent to �5.

15. Name all angles congruent to �4.

16. Name three pairs of angles with sums of 180�.

17. Which line is the transversal?

Homework and PracticeParallel and Perpendicular Lines7A

LESSON

124

35

68

7

x

r

s

12

435

6

87

x

y

a

875

64

31

2

n x

m

8 7

56

43

1 2

a b

m

georgia performance 7a parallel and perpendicular lines · parallel lines perpendicular lines...

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