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Chapter 3: Q27 (page 98)

Prove Theorem 3-11 by using the diagram below. (Begin by stating what is given and what is to be proved. Draw the auxiliary ray shown.)

Short Answer

Expert verified

It is proved that the sum of measures of angles of triangle is 180.

Step by step solution

01

Step 1. Angle addition postulate.

From the given figure, it can be observed that

m∠DCA+m∠4=180and m∠DCA=m∠3+m∠5.

02

Step 2. Description of step.

Substitute m∠3+m∠5for m∠DCAinto m∠DCA+m∠4=180.

m∠3+m∠4+m∠5=180

03

Step 3. Description of step.

If two parallel lines are intersected by a transversal then alternate interior angles are congruent. Therefore,

m∠2≅m∠5m∠1≅m∠4

04

Step 4. Description of step.

Substitute m∠2for m∠5and m∠1for m∠4into step 2.

m∠3+m∠1+m∠2=180m∠1+m∠2+m∠3=180

Hence it is proved that the sum of measures of angles of triangle is 180.

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Most popular questions from this chapter

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

Name five lines that appear to be parallel toAG¯.

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

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

Exercises 23 – 29 refer to the diagram in Step 2 of Exercise 22

Suppose the top and bottom of the box lie in parallel lines. Explain how theorem 3.1 can be used to prove CD¯ ∥ IJ¯.

Exercises 23 – 29 refer to the diagram in Step 2 of Exercise 22

How many pairs of parallel planes are shown?

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

Two lines that are not coplanar intersect.
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