select the correct answer. based only on the facts in the diagram, which triangle criterion can you use to…

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

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

Answer

Explanation:

Step1: Identify equal - sides and angles

In (\triangle ABC) and (\triangle ABD), we have (AB = AB) (common side), (\angle ABC=\angle ABD = 90^{\circ}), and (CB = BD) (indicated by the equal - length marks).

Step2: Recall congruence criteria

The Side - Angle - Side (SAS) 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 two triangles are congruent. Here, the two sides are (CB = BD) and (AB=AB), and the included right - angle (\angle ABC=\angle ABD).

Answer:

A. SAS