Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 10 - Section 10.4 - Analytic Proofs - Exercises - Page 464: 3

Answer

The diagonals of squares are always perpendicular bisectors.

Work Step by Step

First, we draw a square, putting one side on the positive x axis and another side on the positive y axis. We then create bisectors of each angle (these are also the diagonals). Since the bases angles of each of the triangles created are bisected, each triangle has two 45 degree angles. From this, it follows that the diagonals formed are perpendicular, for the sum of all of the angles in a triangle is 180 degrees.
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