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

HL
LL
HA
LA

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

Name of postulate or theorem that supports the conclusion that the triangles are congruent is Angle-side-Angle (ASA).

Given information:

$\angle C,\; \angle F$ are right triangle, $AC=DF;\angle B=\angle E$

From the figure,

$\Delta ACB\;\&\;\Delta DFE$ are right angle triangle.

$AC=DF \;\;\;\;\{\rm{given}\} \\\angle B=\angle E \; \;\;\;\;\{\rm{given}\}$

And $\angle C=\angle F=90^\circ$

$\Delta ACB\;\cong\;\Delta DFE$                 {$ASA$ congruence rule}

Hence, Name of postulate or theorem that supports the conclusion that the triangles are congruent Angle-side-Angle.

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