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Elementary Geometry for College St...

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

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BuyFindarrow_forward

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

Chapter 1.7, Problem 27E, In Exercises 27 to 35, complete the formal proof of each theorem. If two angles are complementary to

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. m1+m3=90°m2+m3=90° 2. Sum of two complementary angles is 90°.
3. m1+m3=m2+m3 3. Substitution
4. m1=m2 4

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