Marcus and Marlee are comparing two right triangles to determine if they are congruent. Marcus has △ABC with a right angle at B . Side AB¯¯¯¯¯¯¯¯ has 2 tick marks, and the hypotenuse has 1 tick mark. Marlee has △PQR with a right angle at Q . Side QR¯¯¯¯¯¯¯¯ has 2 tick marks, and the hypotenuse has 1 tick mark. Marcus says the triangles are congruent by the HL Congruence Theorem, but Marlee does not agree. Who is correct

Answer 1

Marcus is correct. The HL (Hypotenuse-Leg) Congruence Theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent. In this case, both triangles have a leg with 2 tick marks and a hypotenuse with 1 tick mark, so they satisfy the criteria for the HL Congruence Theorem. Therefore, the triangles are congruent.