   Chapter 3.3, Problem 46E ### 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 Exercises 44 to 46, explain why each statement is true.The bisectors of the base angles of an isosceles triangle, together with the base, form an isosceles triangle.

To determine

To explain:

The bisectors of the base angles of an isosceles triangle, together with the base, form an isosceles triangle.

Explanation

Procedure used:

(1) If two congruent angles are bisected, then the bisected parts of angles are also congruent.

(2) If two angles of a triangle are congruent, then the triangle is an isosceles triangle.

Given:

An isosceles ΔPMN is given and MQ¯ bisects M and NQ¯ bisects N.

Figure (1)

Calculation:

ΔPMN is an isosceles triangle.

MNmM=mN (1)

MQ¯ bisects M.

mQMN=12mMmM=2(mQMN)

NQ¯ bisects N

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