Geometry: Common Core (15th Edition)

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

Chapter 4 - Congruent Triangles - 4-6 Congruence in Right Triangles - Lesson Check - Page 261: 2


Yes, the two triangles are congruent. We can write the congruence statement as follows: $\triangle PML ≅ \triangle NMO$

Work Step by Step

In these triangles, $\angle NMO$ is a right angle, but we can say that $\angle PML$ is also a right angle because they are vertical angles, and vertical angles are congruent. Additionally, $\overline{ML}$ and $\overline{MO}$ are congruent, and the hypotenuses $\overline{LP}$ and $\overline{ON}$ are also congruent. This means that $\triangle PML ≅ \triangle NMO$ because of the hypotenuse-leg theorem, which states that if one leg and the hypotenuse of a right triangle are congruent to one leg and the hypotenuse of another right triangle, then the triangles are congruent.
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