Question

based only on the facts in the diagram, which triangle criterion can you use to prove that \\( \triangle abc \\) and \\( \triangle abd \\) are congruent?
a. sas
b. saa
c. asa
d. sss

Explanation:

Step1: Identify the given information

From the diagram, we have \(CB = BD\) (marked as equal), \(\angle ABC=\angle ABD = 90^{\circ}\) (right angles), and \(AB\) is a common side.

Step2: Recall the SAS criterion

The SAS (Side - Angle - Side) criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
In \(\triangle ABC\) and \(\triangle ABD\), \(CB = BD\), \(\angle ABC=\angle ABD\), and \(AB = AB\) (common side).

Answer:

A. SAS