Question

select the correct answer. based only on the facts in the diagram, which triangle criterion can you use to prove that δabc and δabd are congruent? a. sas b. saa c. asa d. sss

Explanation:

Step1: Analyze the diagram

From the diagram, we see that \( CB = BD \) (marked with the same tick), \( \angle ABC=\angle ABD = 90^\circ\) (right angles), and \( AB \) is a common side to both \(\triangle ABC\) and \(\triangle ABD\).

Step2: Identify the congruence criterion

The SAS (Side - Angle - Side) congruence 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 triangles are congruent. Here, we have \( CB = BD\) (side), \( \angle ABC=\angle ABD\) (angle, included between the sides \( CB - AB\) and \( BD - AB\)), and \( AB = AB\) (side). So, the SAS criterion is satisfied.

Answer:

A. SAS