Is it possible for a right triangle with a leg that is 12 inches long and a hypotenuse that is 37 inches long to be congruent to a right triangle with a leg that is 35 inches long and a hypotenuse that is 37 inches long? Complete the explanation. Yes
. Let the remaining leg of the first triangle have a length of x inches. Then by the Pythagorean Theorem, x2 + 122 = 372. So, x2 + 144 = 1,369, x2 = 1,225, and x =
. Therefore, the hypotenuse and a leg of the first right triangle are congruent to the hypotenuse and a leg of the second right triangle, so the triangles
are
congruent by the HL Triangle Congruence Theorem.