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Chapter 3: Q12 (page 87)

In each exercise some information is given. Use this information to name the segments that must be parallel. If there are no such segments, write none.

∠7and ∠EFBare supplementary.

Short Answer

Expert verified

The required segments areCE¯andBF¯

Step by step solution

01

Step 1. Extract the angles related to angle EFB

The angle ∠EFBconsists of two angles which are ∠8and ∠9which mean that the addition measurement of these angles will be equal to ∠EFB.

∠EFB=∠8+∠9

02

Step 2. Determine the angles that are having the equal measurement

Determine the addition of measurement of angles present on the straight line AFE.

∠10+∠8+∠9=180

Make an equation by using the angles present in∠EFBand the provided property of the angles.

∠7+∠8+∠9=180

Compare the obtained equations ∠10+∠8+∠9=180and ∠7+∠8+∠9=180∠7=∠10.

∠7=∠10

03

Step 3. Determine which theorem or postulate can be used

The postulate 10 can be used which states that two angles represents the corresponding angles only when a separate line travels through these two lines which are having a parallel relation between them.

04

Step 4. Make the conclusion

According to the postulate and obtained equal angles the parallel segments are CE¯and BF¯.

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Most popular questions from this chapter

State the postulate or theorem that justifies each statement.

∠3 is supplementary to∠5

Name five lines parallel to plane ABCD

Use two lines of notebook paper as parallel lines and draw any

transversal. Use a protractor to measure

Measure one pair of same side interior angles. Repeat the experiment with another transversal. What appears to be true?

Classify each pair of angles as alternate interior, same side interior or corresponding angles

and

Classify each pair of angles as alternate interior, same side interior

or corresponding angles

and

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