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: 1


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

Work Step by Step

In these triangles, $\angle B$ and $\angle C$ are both right angles, $BC$ and $EF$ are both $6$, and the hypotenuses $AC$ and $FD$ are both $10$. This means that $\triangle ABC ≅ \triangle FED$ 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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