Chapter 10.4, Problem 11E

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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 midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle.

To determine

**To answer:**

The analytic proof for the given theorem “The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle”.

Explanation

Given theorem is,

The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle.

The above figure shows the right triangle ABC.

The vertices of the triangle ABC is A

AB is the hypotenuse of the right triangle.

And D is the midpoint of the hypotenuse AB.

Hence,

Based on the midpoint formula,

The midpoint of AB

The midpoint of AB

Based on the distance formula, the length of AD as below,

AD

AD

AD

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