Question

here are two triangles. which statement is true? △bac≅△dca by the asa congruence postulate. △bac≅△dca by the sas congruence postulate. △bac≅△dac by the asa congruence postulate. △bac≅△dac by the sas congruence postulate.

Explanation:

Step1: Identify the sides and angles

In \(\triangle BAC\) and \(\triangle DAC\):

• \(AB = AD\) (marked as equal)
• \(\angle BAC=\angle DAC\) (marked as equal)
• \(AC = AC\) (common side)

Step2: Apply the SAS Congruence Postulate

The Side - Angle - Side (SAS) Congruence Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Here, in \(\triangle BAC\) and \(\triangle DAC\), we have two sides (\(AB = AD\), \(AC = AC\)) and the included angle (\(\angle BAC=\angle DAC\)) congruent.

Answer:

\(\triangle BAC\cong\triangle DAC\) by the \(SAS\) Congruence Postulate.