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.

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.

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