   Chapter 3.3, Problem 45E ### 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 46 to 48, explain why each statement is true.The bisector of the vertex angle of an isosceles triangle bisects the base.

To determine

To explain:

The bisector of the vertex angle of an isosceles triangle bisects the base.

Explanation

(1) If two angles and the included side of one triangle are congruent to two angles and the included sides of a second triangle, then the triangles are congruent (ASA).

(2) If two sides of a triangle are congruent, then the angles opposite these sides are also congruent.

Given:

An isosceles ΔABC is given with the vertex angle bisector AD¯ and AB¯AC¯.

Figure (1)

Approach:

Consider the ΔABC with the vertex angle bisector AD¯

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