   Chapter 1.6, Problem 4E ### 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 Exercise 3 and 4, supply statements. Given: m ∠ A O B ≅ m ∠ 1 m ∠ B O C ≅ m ∠ 1 Prove: O B → bisects ∠ A O C PROOF Statements Reasons 1. ? 1. Given 2. ? 2. Substitution 3. ? 3. Angles with equal measures are congruent. 4. ? 4. If a ray divides an angle into two congruent angles, then the ray bisects the angle.  To determine

To prove:

That OB bisects AOC and give the statements in the table form.

Explanation

Given:

mAOBm1

mBOCm1

And,

The given figures are,

Figure (1)

Figure (2)

The given table is shown below.

 PROOF Statements Reasons 1. ? 1. Given 2. ? 2. Substitution 3. ? 3. Angles with equal measures are congruent. 4. ? 4. If a ray divides an angle into two congruent angles, then the ray bisects the angle.

Property used:

a. The Additive Property of Equality states that if same number is added to both sides of the equation then the sides of the equation remains equal.

b. If the measure of two angles is equal then the angles are known as congruent angles.

c. According to Substitution Property, if x=y, then x can be substituted for y and y can be substituted for x in any equation.

Approach:

The reason for the first statement of the proof is “Given”. So, the given statements are,

mAOBm1

mBOCm1

The reason for the second statement of the proof is “Substitution” and the angle 1 is same for both the angles.

So, the measures of angles can be written as,

mAOB=mBOC

The reason for the third statement of the proof is “Angles with equal measures are congruent”

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