Chapter 10.4, Problem 6E

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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 medians to the congruent sides of an isosceles triangle are equal in length.

To determine

**To answer:**

The analytic proof for the given theorem “The medians to the congruent sides of an isosceles triangle are equal in length”.

Explanation

Given theorem is,

The medians to the congruent sides of an isosceles triangle are equal in length.

The above graph shows the isosceles triangle ABC.

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

Hence,

Let E and D be the mid points of the sides of AC and BC.

Joining AD and BE and which is the median to the congruent sides of the isosceles triangle as shown in the graph.

To prove that

Considering the two triangles ACD and BCE:

Where,

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