Question

Choose the abbreviation of the postulate or theorem that supports the conclusion that the triangles are congruent.

Given:

∠C, ∠F are rt. ∠'s; AC = DF; ∠B = ∠E

Answer 1

The HL (Hypotenuse-Leg) Congruence Theorem supports the conclusion that the triangles are congruent based on the given right angles, a pair of equal sides, and a pair of equal acute angles.

Step-by-step explanation:

The question requires us to use a postulate or theorem to conclude that two triangles are congruent based on the given information: one right angle in each triangle, one pair of corresponding sides equal, and one pair of corresponding acute angles equal. This information aligns with the HL (Hypotenuse-Leg) Congruence Theorem, a specific case of congruence for right-angled triangles.

To apply the HL theorem, we need to establish that two triangles have a congruent hypotenuse and one congruent leg. Since ∠C and ∠F are right angles, AC and DF are the hypotenuses, while ∠B = ∠E indicates that another pair of corresponding sides is congruent. Therefore, based on the HL Congruence Theorem, we can conclude that the triangles are congruent.