Chapter 10.4, Problem 2E

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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 opposite sides of a parallelogram are equal in length.

To determine

**To answer:**

The analytic proof for the given theorem “The opposite sides of a parallelogram are equal in length”.

Explanation

Given theorem is,

The opposite sides of a parallelogram are equal in length.

The above graph shows the parallelogram ABCD.

From the theorem the length of the opposite sides of the parallelogram are equal and expressed as below,

Opposite side of

And the opposite side of

The coordinates of the figure are

In order to prove “The opposite sides of a parallelogram are equal in length”, needed to use distance formula.

Length of

Using distance formula for finding length of the diagonal

Where,

Simplifying the above equation,

Similarly,

Simplifying the above equation,

Hence,

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