Elementary Geometry for College Students (5th Edition)

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

Chapter 10 - Review Exercises - Page 491: 33

Answer

If the diagonals of a given rectangle are perpendicular, the shape is a square.

Work Step by Step

We name the vertices: $A:(0,0) \\ B: (0,b) \\ C: (a,b) \\ D: (a,0)$ We see if a is equal to b. Since the lines are perpendicular, it follows that the product of their slopes is $-1$: $ m_1= \frac{b-0}{a-0} = \frac{b}{a}$ $ m_2= \frac{b-0}{0-a} = \frac{b}{-a}$ Thus: $\frac{b}{-a} \times \frac{b}{a} = -1$ This is only true when a and b are equal, so we see that the shape is a square.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.