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Chapter 3: Q9 (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.

m∠8+m∠5+m∠6=180

Short Answer

Expert verified

The required segments are FE¯and CD¯.

Step by step solution

01

Step 1. Extract the measurement of angles related to the triangle FEC

The triangle FEC consist of three angles which are ∠8, ∠5and ∠7which means that the addition measurement of these angles will be equal to 180.

m∠8+m∠5+m∠7=180

02

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

Compare the obtained equation m∠8+m∠5+m∠7=180with the provided equation.

m∠7=m∠6

03

Step 3. Determine which theorem or postulate can be used

The theorem 3-5 can be used which states that the relation between two lines is parallel only when a separate line travels through these two lines and the angles which are positioned on the alternate interior side represents the congruent angles.

04

Step 4. Make the conclusion

According to the theorem and obtained equal angles the parallel segments are FE¯and CD¯.

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Most popular questions from this chapter

Assume that a∥band c∥d.

If m∠7=x, then m∠12=?¯and m∠6=?¯

Complete each statement with the word always, sometimes, or never.

Two lines skew to a third line are skew to each other

Exercises 23-29 refer to the diagram in step 2 of exercise 22.

Name five lines that appear to be parallel toAG¯.

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

and

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

and

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