Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 10 - Section 10.4 - Analytic Proofs - Exercises - Page 480: 15

Answer

When the midpoint of a rectangle is joined to the two intersections of the other two sides, an isosceles triangle is formed.

Work Step by Step

We call the length of the rectangle on the x-axis 2a, and we call the height of the rectangle 2b. Thus, we find that its midpoint (for the side opposite the x-axis) is $(a,b)$. Thus, each line drawn inside the rectangle is part of a right triangle where one leg is of length a and the other leg is of length b. Thus, the two line segments drawn are congruent, so the shape formed is a right triangle.
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