   Chapter 10.4, Problem 14E ### 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 1 to 17, complete an analytic proof for each theorem.The perpendicular bisector of the base of an isosceles triangle contains the vertex of the triangle.

To determine

The analytic proof for the given theorem “The perpendicular bisector of the base of an isosceles triangle contains the vertex of the triangle”

Explanation

Given theorem is,

The perpendicular bisector of the base of an isosceles triangle contains the vertex of the triangle.

The above graph shows the isosceles triangle ABC.

In an isosceles triangle ABC, the side length of AC and BC are equal.

Hence, AC=BC.

Where, the perpendicular bisector D is drawn to the base as shown in the figure.

The coordinates of the triangle ABC is A (0, 0), B (2a,0) and C (a,b).

The perpendicular bisector D is also the midpoint of the base AB

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