Chapter 10.CR, Problem 35CR

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

*Prove the statements in Review Exercises 32 to 36 using analytic geometry.*

If two medians of a triangle are equal in length, then the triangle is isosceles.

To determine

**To answer:**

The analytic proof for the given theorem “If two medians of a triangle are equal in length, then the triangle is isosceles”.

Explanation

Given theorem is,

If two medians of a triangle are equal in length, then the triangle is isosceles.

Condition of isosceles triangle

The above graph shows the triangle ABC.

The coordinates of the triangle

In a triangle ABC, the side length of AC and BC are equal and congruent. That can be proved using distance formula as below,

Length of AC

Length of AC

Length of AC

Length of AC

Length of AC

Similarly the length BC as below,

Length of AC

Length of AC

Length of AC

Length of AC

Length of AC

Similarly the length AB as below,

Length of AB

Length of AB

Length of AB

Length of AB

Hence,

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