Question

If two pairs of corresponding sides of two right triangles are congruent, then the triangles are congruent. Is this statement always, sometimes, or never true? explain your reasoning.
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Answer 1

This statement is true SOMETIMES.

REASON: We have 2 pairs of corresponding sides that are congruent and one angle is equal. These triangles can be congruent only by the SAS (Side Angle Side) congruency which occurs only when the equal angle is situated in between the congruent sides. This statement is possible only when the sides other than the hypotenuse are the congruent sides. Thus, there is only one possibility of this statement being true.