Question

If the two legs of a right triangle measure 5 and 12 respectively, and the leg and hypotenuse of another right triangle measure 12 and 13 respectively, explain why the triangles would be congruent.

Answer 1

They would be congruent by the side side side (s-s-s) theorem.
They are BOTH right triangles.
You have one triangle with legs = 5 and 12, by the Pythagorean Theorem, the hypotenuse would be 13.
In the other triangle, you have a leg = 12 and hypotenuse = 13.  By the Pythagorean Theorem, the other leg would be 5.
So, you have 2 triangles with sides of 5, 12 and 13 and they are congruent by the (s-s-s) theorem.