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In $ΔABC$ and $ΔDEF$ , AB = DF and $∠ A = ∠ D$ . The two triangles will be congruent by SAS axiom if:

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AC = DE

AC = EF

BC = EF

BC = DE

answer is B.

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Detailed Solution

Given that, in

ΔABC

and

ΔDEF

, AB = DF and

∠ A = ∠ D

For triangle to be congruent

SAS

(Side angle Side) axiom, we need to have two equal sides and the included angle same.
In

ΔABC

and

ΔDFE,

We have

AB = DF

and

∠ A = ∠ D

But

∠ A

is formed by the two sides AB and AC of

ΔABC .

∠ D

is formed by the two sides DE and DF of

ΔDFE

.
So we need

AC = DE

for the two triangles to be congruent.
Thus, the two triangles will be congruent by SAS axiom if AC=DE.
Therefore, the correct option is 2.

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