   Chapter 1.5, Problem 31E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

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 complementary to ∠ 2 PROOF Statements Reasons 1. B A → ⊥ B C → 1. ? 2. ? 2. If two rays are ⊥ , then they meet to form a right ∠ 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. BA→⊥BC→ 1. Given 2. ∠ABC is a right angle 2. If two rays are ⊥, then they meet to form a right ∠ 3. m∠ABC=90° 3. The measure of a right angle is 90°. 4. m∠ABC=m∠1+m∠2 4. Angle-addition postulate 5. m∠1+m∠2=90° 5

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