   Chapter 1.7, Problem 27E ### 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 complementary to the same angle, then these angels are congruent. Given: ∠ 1 is complementary to ∠ 3 ∠ 2 is complementary to ∠ 3 Prove: ∠ 1 ≅ ∠ 2 PROOF Statements Reasons 1. ∠ 1 is complementary to ∠ 3 ∠ 2 is complementary to ∠ 3 1. ? 2. m ∠ 1 + m ∠ 3 = 90 m ∠ 2 + m ∠ 3 = 90 2. ? 3. m ∠ 1 + m ∠ 3 = m ∠ 2 + m ∠ 3 3. ? 4. m ∠ 1 = m ∠ 2 4. ? 5. ∠ 1 ≅ ∠ 2 5. ?

To determine

To find:

The complete formal proof of the given theorem.

Explanation

Given:

The statement of given theorem is,

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

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

Prove: 12

Definition:

If the sum of two angles is 90° then the angles are known as complementary angles.

Approach:

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

 Statements Reasons 1. ∠1 is complementary to ∠3∠2 is complementary to ∠3 1. Given 2. m∠1+m∠3=90°m∠2+m∠3=90° 2. Sum of two complementary angles is 90°. 3. m∠1+m∠3=m∠2+m∠3 3. Substitution 4. m∠1=m∠2 4

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