   Chapter 10.4, Problem 3E 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 square are perpendicular bisectors of each other.

To determine

The analytic proof for the given theorem “The diagonals of a square are perpendicular bisectors of each other”.

Explanation

Given theorem is,

The diagonals of a square are perpendicular bisectors of each other.

The above graph shows the square ABCD.

The coordinates of the square is A0, 0, Ba, 0, C(a, b) and D(0, b).

The diagonals AC and BD are joined as shown in the figure.

Condition for diagonal to be perpendicular is,

m1·m2=-1

Let m1 be the slope of the diagonal AC.

And Let m2 be the slope of the diagonal BD

Formula for slope of the line is m=y2-y1x2-x1

x1, y1=(0, 0)

x2, y2=(a,

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