Chapter 10.CR, Problem 34CR

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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

If the diagonals of a trapezoid are equal in length, then the trapezoid is an isosceles trapezoid.

To determine

**To answer:**

The analytic proof for the given theorem “If the diagonals of a trapezoid are equal in length, then the trapezoid is an isosceles trapezoid”.

Explanation

Given theorem is,

If the diagonals of a trapezoid are equal in length, then the trapezoid is an isosceles trapezoid.

The above graph shows the trapezoid ABCD.

The coordinates of the trapezoid are

The diagonals

**To prove:**

If

Characteristic of isosceles trapezoid:

i. The length of the diagonal are should be equal in length

ii. The lower and the upper bases are should be in parallel.

In the trapezoid ABCD in which base angles are equal and therefore left and right side lengths are equal.

Hence,

The lower and upper bases

And the Length of the diagonal

Using distance formula for finding length of the diagonal

Where,

Simplifying the above equation,

Where,

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