Look at the figure. how can you prove ∆abd and ∆acd are congruent?

a. ∆abd ≅ ∆acd by the sas postulate.

b. it is not possible to determine if the triangles are congruent.

c. ∆abd ≅ ∆acd by the sss postulate.

 The correct option is (B).  It is not possible to determine if the triangles are congruent.

Step-by-step explanation:  We are given to select the correct option by which we can prove that ∆ABD and ∆ACD are congruent.

As shown in the figure,

In ∆ABD and ∆ACD, we have

∠ADB = ∠ADC = 90°,

AD is the common side.

So, one angle and the adjacent side of one triangle are congruent to the corresponding angle and the adjacent side of the other triangle.

That is, to prove that the two triangles are congruent, we need one of the following two conditions:

(i)  BD = CD

or

(ii) ∠BAD = ∠CAD.

Since none of these two are given, so we cannot determine the congruence of the two triangles.

Therefore, it is not possible to determine if the triangles are congruent.

Thus, option (B) is correct.