Question

4 - 6 congruence in right triangles
are the triangles shown at the right congruent? explain.
a. yes, by ssa.
b. yes, by the hl theorem.
c. no; ssa cannot be used because there is only one pair of congruent corresponding sides.
d. no; the hl theorem cannot be used because there is only one pair of congruent legs.

Explanation:

Step1: Recall congruence theorems

SSA (Side - Side - Angle) is not a valid congruence theorem for non - right triangles in general. For right - triangles, we have the HL (Hypotenuse - Leg) theorem.

Step2: Check conditions for HL

The two triangles are right - triangles (they have right angles). The hypotenuses are marked as congruent (the sides with the cross - marks) and they share a common leg (the side between the right angle and the hypotenuse). So, by the HL (Hypotenuse - Leg) theorem, the triangles are congruent.

Answer:

B. Yes, by the HL Theorem.