Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 4 - Section 4.3 - The Rectangle, Square, and Rhombus - Exercises - Page 195: 40a


The right triangle is in blue. Since it is a midpoint, clearly it is equidistant from the vertices that are opposite the 90 degree angle. Thus, we must prove that triangle AEB is isosceles. Since angle A and angle B are both bisected 90 degree angles, they have equal measures. Since the base angles are the same, it is isosceles. Thus, the midpoint of the hypotenuse is equidistant from the vertices.

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