We are asked to name the postulate we would use to prove that the given triangles are congruent. To do so, we will start by labeling the vertices in the given diagram.
Looking at the given markings, we can see that AB and AD are congruent as well as CB and CD. Additionally, BD is congruent to itself by the Reflexive Property of Congruence.
AB ≅ AD
CB ≅ CD
BD ≅ BD
However, except BD, there is no congruent corresponding part in the different triangles. Therefore, it is not possible to prove that the triangles are congruent.
