Question

What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate?

Answer 1

Answer:

<CBA = <CDA

Step-by-step explanation:

Using <CBA = <CDA and Base angle theorem, you can say that AB = AD.

Now you have <CBA = <CDA, AB = AD, and CB = CD. These prove SAS.

Answer 2

Answer:

Option D.

Step-by-step explanation:

Given information: $\overline {BC} \cong \overline {DC}$

Property of isosceles triangle : In a triangle, if two angles are congruent, then sides opposite those angles are congruent.

If $\angle CBA\cong CDA$, then $\overline {AB} \cong \overline {AD}$.

Let as consider $\angle CBA\cong CDA$ is given.

In triangle ABC and CDA

$\overline {BC} \cong \overline {DC}$         (Given)

$\angle CBA\cong CDA$                (Given)

$\overline {AB} \cong \overline {AD}$           (Property of isosceles triangle)

Two sides of a triangle and included angle are congruent to corresponding sides and included of another triangle.

$\triangle ABC\cong \triangle ADC$           (By SAS)

Therefore, the correct option is D.