Question

Based on the given information and the algebraic and geometric properties presented or proven thus far, choose the congruence theorem that could be used to prove the triangles congruent. If it is not possible to prove the triangles are congruent, choose "not possible".

SSS
SAS
SSA
not possible

Answer 1

Your answer would be (B) Side Angle Side or (SAS)

Answer 2

The correct option is 2.

Explanation:

Given information: DC║AB, DC=AB.

If a transversal line intersect two parallel lines, then the alternative interior angles are equal.

In triangle ABC and CDA,

`AB=DC` (Given)

`\angle 2=\angle 3` (Alternative interior angles)

`CA=CA` (Common side)

Two corresponding sides and their including angle are equal.

By SAS postulate of congruent triangles,

`\triangle ABC\cong \triangle CDA`

Since both triangles are congruent by SAS postulate, therefore the correct option is 2.