Question

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

Answer 1

∠C and ∠F are right angles. So, the triangles are right triangles.

AC = DF are the short legs of both triangles.

∠B = ∠E.

In this scenario, the postulate is ASA (Angle-Side-Angle)

The remaining sides that must be noted to prove that the triangles are congruent are the long legs and hypotenuse.

CB = FE can be LL for congruence where tt states that if the legs of one right triangle are congruent to the legs of another right triangle, then the triangles are congruent.

Answer 2

Answer:  LA

Step-by-step explanation:

Given:  In ΔABC  and  ΔDEF

∠C, ∠F are right angles

⇒ Both triangles are right triangles.

 AC = DF  ;  ∠B = ∠E

By LA theorem, we get

ΔABC  ≅  ΔDEF

• The LA theorem tells that for any two right triangles, where one acute angle and a leg of one of the triangles are congruent to an angle and a leg of the other triangle, then the two triangles are congruent.

Hence, LA is the abbreviation of the theorem that supports the conclusion that the triangles are congruent.