Question

name the postulate that makes the triangles congruent.

Explanation:

Looking at $\triangle ABC$ and $\triangle ADC$:

1. $\angle BAC = \angle DAC$ (marked equal angles at vertex $A$)
2. $AB = AD$ (marked equal sides)
3. $\angle ABC = \angle ADC$ (marked equal right angles)

This matches the AAS (Angle-Angle-Side) congruence postulate, where two angles and a non-included side of one triangle are equal to the corresponding two angles and non-included side of another triangle.

Answer:

AAS