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; bc = ef. Options: A. LA B. HA C. LL D. HL

Answer 1

The triangles are congruent because of the HL postulate.

Step-by-step explanation:

The given information tells us that angle C and angle F are right angles (rt. ∫'s), and that segments AC and DF have equal lengths, as well as segments BC and EF. This situation can be supported by the HL (Hypotenuse-Leg) postulate. According to the HL postulate, 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, since the right triangles ACB and DFE satisfy these conditions, we can conclude that the triangles are congruent.

Answer 2

The HL (Hypotenuse-Leg) theorem supports the conclusion that the two triangles are congruent because they have a right angle and two corresponding sides equal (one hypotenuse and one leg each).

Step-by-step explanation:

The correct abbreviation of the postulate or theorem that supports the conclusion that the triangles are congruent, given that ∠c, ∠f are right angles; ac = df; and bc = ef, is HL (Hypotenuse-Leg) congruence theorem. This theorem states that in right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, then the triangles are congruent. Since both given triangles have a right angle and two corresponding sides (one hypotenuse and one leg) are congruent, they are indeed congruent by the HL congruence theorem.