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

In the diagram, we have \( \triangle ABC \) and \( \triangle ABD \). \( AB \) is common to both triangles. \( \angle ABC \) and \( \angle ABD \) are right angles (so they are equal). The segments \( BC \) and \( BD \) are marked as equal (indicated by the red ticks).

Step2: Identify the congruence criterion

We have two sides and the included angle: \( AB = AB \) (common side), \( BC = BD \) (given), and \( \angle ABC=\angle ABD = 90^\circ \) (included angle between the two sides). 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