Elementary Geometry for College Students (6th Edition)

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

Chapter 5 - Section 5.3 - Proving Lines Parallel - Exercises - Page 233: 42


The proof is in the following form: Column 1 of proof; Column 2 of proof. Thus, we have: 1. The midpoint of both sides breaks the sides into even segments; definition of a midpoint. 2. The two sides of the original triangle are proportional to the two sides of the new triangle; this follows from (1). 3. The angle shared is congruent to itself; identity property 4. The two triangles are similar; SAS

Work Step by Step

By theorem the segment joining two midpoint of two sides of a triangle is parallel to the base. Therefore, the corresponding angles are congruent $ \angle M = \angle N $ the two triangles AMN and ABC are similar by AA. $\square$
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