Elementary Geometry for College Students (6th Edition)

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

Chapter 8 - Section 8.1 - Area and Initial Postulates - Exercises - Page 350: 33

Answer

There are many similar triangles.

Work Step by Step

Using the fact that M, N, and P are all midpoints, we find that all of the smaller sets of sides are congruent, meaning that all of the 4 smaller triangles are congruent by SSS. Because ABC contains four of the smaller triangles, this means that its area is 4 times are great as the area of one of the smaller triangles, triangle MNP.
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