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Math
GeometryElementary Geometry for College Students6th Edition

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

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
BuyFindarrow_forward

Elementary Geometry for College St...

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 diagonals of an isosceles trapezoid are equal in length.

To determine

To answer:

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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