Elementary Geometry for College Students (6th Edition)

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

Chapter 10 - Section 10.4 - Analytic Proofs - Exercises - Page 464: 1


The diagonals have an equal length when the figure is a rectangle.

Work Step by Step

We place the rectangle at the origin, giving it length a for its short sides and length b for its long sides. Using the Pythagorean theorem, we obtain: $(d_1)^2 = a^2 + b^2 \\ (d_2) ^2 = a^2 +b^2$ Combining these gives: $(d_1)^2 = (d_2)^2 \\ d_1 = d_2$ Hence, the diagonals are equal in length.
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