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: 55


$\frac{n}{h} = \frac{h}{m}$

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 $n$ is the longer leg of the larger triangle formed by the altitude of the large triangle, and $h$ is the shorter leg of that same triangle. Additionally, $h$ is the longer leg of the smaller triangle formed by the altitude 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: $\frac{n}{h} = \frac{h}{m}$
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