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91Ó°ÊÓ

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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