Question

4 - 8 congruence in right triangles
why do we not use a leg - leg (ll) theorem that says if you know that the legs of two right triangles are congruent, then the triangles are congruent?
a. this information is not sufficient to prove triangles congruent.
b. this case is already covered by the hl theorem.
c. this case is already covered by the sss postulate.
d. this case is already covered by the sas postulate.

Explanation:

The Leg - Leg (LL) Theorem for right - triangle congruence is a special case. In general, for congruence of triangles, we have postulates like SAS (Side - Angle - Side), SSS (Side - Side - Side), etc. If two legs of right - triangles are congruent, then the triangles are congruent. But this is already covered by the SAS postulate. In a right - triangle, if we consider the right angle (the included angle) and the two legs (the sides of the included angle), then by the SAS postulate, if two legs (sides) and the included right angle (angle) of two right - triangles are congruent, the triangles are congruent.

Answer:

D. This case is already covered by the SAS Postulate.