   Chapter 1.6, Problem 1E ### 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 1 and 2, supply reasons. Given: ∠ 1 ≅ ∠ 3 Prove: ∠ M O P ≅ ∠ N O Q PROOF Statements Reasons 1. ∠ 1 ≅ ∠ 3 1. ? 2. m ∠ 1 ≅ m ∠ 3 2. ? 3. m ∠ 1 + m ∠ 2 = m ∠ M O P and m ∠ 2 + m ∠ 3 = m ∠ N O Q 3. ? 4. m ∠ 1 + m ∠ 2 = m ∠ 2 + m ∠ 3 4. ? 5. m ∠ M O P = m ∠ N O Q 5. ? 6. ∠ M O P ≅ ∠ N O Q 6. ? To determine

To prove:

That MOP=NOQ and give the reasons in the table form.

Explanation

Given:

The given figure is,

Figure (1)

The given table is shown below.

 PROOF Statements Reasons 1. ∠1≅∠3 1. ? 2. m∠1=m∠3 2. ? 3. m∠1+m∠2=m∠MOPAndm∠2+m∠3=m∠NOQ 3. ? 4. m∠1+m∠2=m∠2+m∠3 4. ? 5. m∠MOP=m∠NOQ 5. ? 6. ∠MOP≅∠NOQ 6. ?

Property used:

a. The Transitive Property of Congruence states that if two angles are each congruent to a third angle, then they are congruent to each other.

b. 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.

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

d. 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 first statement of the proof is given. That is.

13

It means the angles 1 and 3 are congruent, so the reason for the first statement is Given.

The second statement of the proof is given. That is.

m1=m3

It means that the two angles are congruent then the measures of those angles will be same so, the reason for the second statement is “If two s are , then they are equal in measure”.

The third statement of the proof is given. That is.

m1+m2=mMOP

And,

m2+m3=mNOQ

In the third statement N is the interior of MOP so, according to Angle-Addition Postulate the sum of 1 and 2 is equal to MOP

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