   Chapter 10.4, Problem 4E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 1 to 17, complete an analytic proof for each theorem.The diagonals of an isosceles trapezoid are equal in length.

To determine

The analytic proof for the given theorem “The diagonals of an isosceles trapezoid are equal in length”.

Explanation

Given theorem is,

The diagonals of an isosceles trapezoid are equal in length.

The above graph shows the isosceles trapezoid ABCD.

From the theorem the diagonals of the isosceles trapezoid is equal and express as below,

AC=BD

The coordinates of the figure are A0, 0, Ba,0, Cd, c and D(b, c).

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

Hence, d=b-a

In order to prove “The diagonals of an isosceles trapezoid are equal in length”, needed to use distance formula.

Length of the diagonal AC= length of the diagonal BD.

Using distance formula for finding length of the diagonal AC.

Where, A0, 0 and Cb, c

AC=(d-0)2+(c-0)2

Simplifying the above equation,

AC=(d)2+(c)2

Where, Ba, 0 and D

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