Chapter 10.4, Problem 15E

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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.*

If the midpoint of one side of a rectangle is joined to the endpoints of the opposite side, then an isosceles triangle is formed.

To determine

**To answer:**

The analytic proof for the given theorem “If the midpoint of one side of a rectangle is joined to the endpoints of the opposite side, then an isosceles triangle is formed”.

Explanation

Given theorem is,

If the midpoint of one side of a rectangle is joined to the endpoints of the opposite side, then an isosceles triangle is formed.

The above figure shows the rectangle ABCD.

The vertices of the rectangle ABCD is A

And M is the midpoint of the side CD.

Joining the midpoint M to the end of the opposite side A and B as shown in above figure and is forming the triangle ABM.

Based on the midpoint formula,

The midpoint of CD

The midpoint of CD

The midpoint of CD

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

MA

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