Chapter 3.3, Problem 46E

### Elementary Geometry for College St...

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

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 Î”PMN is given and MQÂ¯ bisects âˆ M and NQÂ¯ bisects âˆ N.

Figure (1)

Calculation:

Î”PMN is an isosceles triangle.

âˆ Mâ‰…âˆ Nmâˆ M=mâˆ N (1)

MQÂ¯ bisects âˆ M.

mâˆ QMN=12mâˆ Mmâˆ M=2(mâˆ QMN)

NQÂ¯ bisects âˆ N

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