Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 7 - Similarity - 7-5 Proportions in Triangles - Practice and Problem-Solving Exercises - Page 478: 56


$\frac{m}{b} = \frac{b}{c}$

Work Step by Step

All three triangles are similar to one another, meaning that the sides of the triangles are proportional. We can see that $b$ is the hypotenuse of the smaller triangle formed by the altitude of the large triangle. Additionally, $b$ is the shorter leg of the large triangle, and $c$ is the hypotenuse of the large triangle. What we want is the corresponding shorter leg in this smaller triangle, which is represented by $m$. The proportion should read: $\frac{m}{b} = \frac{b}{c}$
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