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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 1.6, Problem 4E
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Elementary Geometry for College St...

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

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Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
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Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
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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.

Chapter 1.6, Problem 4E, In Exercise 3 and 4, supply statements. Given: mAOBm1mBOCm1 Prove: OB bisects AOC PROOF Statements , example 1 Chapter 1.6, Problem 4E, In Exercise 3 and 4, supply statements. Given: mAOBm1mBOCm1 Prove: OB bisects AOC PROOF Statements , example 2

To determine

To prove:

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

Explanation

Given:

m∠AOB≅m∠1

m∠BOC≅m∠1

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,

m∠AOB≅m∠1

m∠BOC≅m∠1

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,

m∠AOB=m∠BOC

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

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