Question

1. suppose ∠bca ≅ ∠eda. using only the information provided in this problem, can you use the sss postulate or the sas postulate to prove △abc ≅ △aed?

neither apply
by sss only
by sas only
both apply

Explanation:

Step1: Check for SAS

We know that in two triangles, if two sides and the included angle are equal, then the triangles are congruent by SAS.
In \(\triangle ABC\) and \(\triangle AED\), we have \(BC = ED\) (given by the marks on the sides), \(\angle BCA=\angle EDA\) (given), and \(AC = AD\) (given by the marks on the sides).
So, \(\triangle ABC\cong\triangle AED\) by SAS.

Step2: Check for SSS

For SSS (Side - Side - Side) congruence, we need to know that all three sides of one triangle are equal to the corresponding three sides of the other triangle.
We only know two pairs of sides (\(BC = ED\) and \(AC = AD\)) from the given information in the problem (the marks on the figure). We do not have information about the third pair of sides (\(AB\) and \(AE\)). So, we cannot use SSS.

Answer:

by SAS only