Elementary Geometry for College Students (6th Edition)

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

Chapter 3 - Section 3.1 - Congruent Triangles - Exercises - Page 128: 6


LL is just a special case of postulate SAS.

Work Step by Step

Each of two right triangles has an angle of $90^{\circ}$. Therefore, for any of two right triangles, they already have a congruent pair of $90^{\circ}$ angles. Therefore, if two right triangles $\triangle A$ and $\triangle B$ also have congruent pairs of legs, they now have 2 congruent sides and a congruent included angle, which is the congruent pair of $90^{\circ}$ angles. So, these two right triangles would be congruent with each other according to postuale SAS. In conclusion, LL is just a special case of postulate SAS.
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