Question

what theorem proves that △abc≅△def? option # 1: asa option # 2: hl option # 3: sas option # 4: ssa

Explanation:

In right - triangles $\triangle ABC$ and $\triangle DEF$, we see that the hypotenuse and one leg of one right - triangle are congruent to the hypotenuse and one leg of the other right - triangle. The Hypotenuse - Leg (HL) theorem states that if the hypotenuse and a leg of a right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent. ASA requires two angles and the included side, SAS requires two sides and the included angle, and SSA is not a valid congruence theorem for general triangles (though it can be in some special cases but not applicable here as a general congruence rule).

Answer:

Option # 2: HL