Which postulate or theorem proves that these two triangles are congruent? asa congruence postulate sas congruence postulate hl congruence theorem aas congruence theorem

ASA Congruence Postulate

Step-by-step explanation:

We have marked that ∠BAE and ∠CDE are congruent.  We also have marked that AE and ED are congruent.  This gives us a side and an angle.

∠AEB and ∠CED are congruent as well; this is because they are vertical angles (opposite angles that share only a vertex).  This gives us two angles and the included side; this is ASA.