   Chapter 10.4, Problem 1E 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 a rectangle are equal in length.

To determine

The analytic proof for the given theorem “The Diagonals of a rectangle are equal in length”.

Explanation

Given theorem is,

The Diagonals of a rectangle are equal in length.

The above graph shows the rectangle ABCD.

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

AC=BD

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

AB- is horizontal and AD- is vertical and the rectangle ABCD is right angle at A.

In order to prove “The Diagonals of a rectangle 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 Ca, c

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

Simplifying the above equation,

AC=(a)2+(c)2

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