Question

Suppose BCA is congruent to EDA. Using only the information provided in this problem, can you use the

SSS Postulate or the SAS Postulate to prove triangle ABC is congruent to triangle AED?

Answer 1

ΔABC and ΔAED are congruent to each other by SAS rule.

Explanation:

We are given a figure in the question.

The figure shows that:

AC = AD, BC = ED, ∠BAC = ∠EAD

We are also given that triangle BCA is congruent to triangle EDA.

Now, we need to prove that triangle ABC is congruent to triangle AED.

We will use SAS criterion of congruence.

In ΔABC and ΔAED,

AC = AD, ∠BAC = ∠EAD, , BC = ED( all given in the figure)

Hence, the two triangles are congruent to each other by SAS rule.

Answer 2

A. By SAS only

Explanation:

Side Side Side postulate (SSS) states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.

Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

In triangles ABC and AED:

• sides ACand AD are congruent (from the diagram);
• angles BCA and EDA are congruent (given);
• sides BC and ED are congruent (from the diagram).

So, SAS postulate can be applied.

SSS postulate cannot be applied, because it is not given that sides AB and AE are conruent.