Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 8 - Section 8.1 - Area and Initial Postulates - Exercises - Page 358: 5

Answer

The altitudes to and to are congruent. This is because QMN and QPN are congruent; corresponding altitudes of congruent triangles are congruent.

Work Step by Step

Draw an altitude from Q on PN at R Draw an altitude from Q on MN at O Let us take altitude $\overline{QR}$ and $\overline{QO}$ Lets compare $\triangle$ QMN and $\triangle$ QPN $\overline{QM}$ = $\overline{PN}$ $\overline{MN}$ = $\overline{PQ}$ $\overline{QN}$ = $\overline{QN}$ (common) By SSS property $\triangle$ QMN and $\triangle$ QPN are congruent Therefore the altitudes to $\overline{PN}$ and $\overline{MN}$ are congruent $\overline{QO}$ and $\overline{QR}$ because we know corresponding altitudes of congruent triangles are equal.
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