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 δabc and δabd 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 δabc and δabd are congruent? a. sas b. saa c. asa d. sss

Answer

Explanation:

Step1: Analyze the diagram

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

Step2: Identify the congruence criterion

We have two sides and the included angle. The side ( AB ) is common, ( CB = DB ), and the included angle between them (( \angle ABC ) and ( \angle ABD )) is equal (both right angles). This matches the SAS (Side - Angle - Side) congruence criterion, where two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Answer:

A. SAS