Question

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

Given:
∠C, ∠F are rt. ∠'s; ∠B = ∠E; BC = EF

HL
LL
HA
LA

Answer 1

(D) LA

Explanation:

Given: ∠C and ∠F are right angles and ∠B=∠E; BC=EF

To find: the abbreviation of the postulate or theorem that supports the conclusion that the triangles are congruent.

Solution:

From the given triangles, ΔABC and ΔDEF,

∠C=∠F=90°(given)

∠B = ∠E(given)

BC = EF (given)

therefore, BC and EF are corresponding legs of these triangles. Also, ∠B = ∠E.

Thus, we have congruent corresponding legs, that are included between right angle and given angle, and corresponding congruent angles, so

we need to use LA (leg-angle) theorem.

Hence, option D is correct.

Answer 2

Because ∠C=∠F = 90⁰,

BC and EF are corresponding legs of these triangles. Also, ∠B = ∠E.

So, we have congruent corresponding legs, that are included between right angle and given angle, and corresponding congruent angles, so

we need to use LA (leg-angle) theorem.