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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 the exterior sides of two adjacent acute angles form perpendicular rays, then these angles are complementary.

Given: B A B C
Prove: 1 is comp to 2

Chapter 1.7, Problem 31E, In Exercises 27 to 35, complete the formal proof of each theorem. If the exterior sides of two

PROOF
Statements Reasons
1. B A B C 1. ?
2. ? 2. If two rays are , then they meet to form a rt
3. m A B C = 90 3. ?
4. m A B C = m 1 + m 2 4. ?
5. m 1 + m 2 = 90 5. Substitution
6. ? 6. If the sum of the measures of two angles is 90 , then the angles are complementary

To determine

To find:

The complete formal proof of the given theorem.

Explanation

Given:

The statement of given theorem is,

If the exterior sides of two adjacent acute angles form perpendicular rays, then these angles are complementary.

Given: BABC

Prove: 1 is complementary to 2

The given figure is,

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. BABC 1. Given
2. ABC is a right angle 2. If two rays are , then they meet to form a right
3. mABC=90° 3. The measure of a right angle is 90°.
4. mABC=m1+m2 4. Angle-addition postulate
5. m1+m2=90° 5

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