   Chapter 1.7, Problem 28E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# In Exercises 27 to 35, complete the formal proof of each theorem.If two angles are supplementary to the same angle, then these angels are congruent. Given: ∠ 1 is supp to ∠ 2 ∠ 3 is supp to ∠ 2 Prove: ∠ 1 ≅ ∠ 3 (HINT: See Exercise 27 for help.) To determine

To find:

The complete formal proof of the given theorem.

Explanation

Given:

The statement of given theorem is,

If two angles are supplementary to the same angle, then these angels are congruent.

Given: 1 is supplementary to 2 and 3 is supplementary to 2

Prove: 13

Definition:

If the sum of two angles is 180° then the angles are known as supplementary angles.

Approach:

The formal proof of given theorem is explained in table below.

 Statements Reasons 1. ∠1 is supplementary to ∠2∠3 is supplementary to ∠2 1. Given 2. m∠1+m∠2=180°m∠2+m∠3=180° 2. Sum of two supplementary angles is 180°. 3. m∠1+m∠2=m∠2+m∠3 3. Substitution 4. m∠1=m∠3 4

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