Question

Look at the figures. How can you prove the triangles are congruent?

∆ABC ≅ ∆DEF by the SSS Postulate.

It is not possible to determine if the triangles are congruent.

∆ABC ≅ ∆DEF by the SAS Postulate.

Answer 1

They are congruent by the "SSS" postulate.

Explanation:

Answer 2

∆ABC ≅ ∆DEF by the SSS Postulate.

Explanation:

The given image shows two triangles which have their corresponding sides congruent. When we have this set-up, we can say by Side-Side-Side postulate (SSS) that those triangles are congruent, because to use this postulate we need all three sides congruent.

The SSS postulate states that if two triangle have all three corresponding sides congruent, then, those triangles are congruent. This deduction means that both triangle have the same sides and angles.

From the congruence we deduct that

`\angle A \cong \angle D\\\angle B \cong \angle E\\\angle C \cong \angle F`

In addition,

`AB \cong DE\\BC \cong EF\\AC \cong DF`

Therefore, the right choice is the first option.