We want to identify a theorem or postulate we can use to prove that triangle △ A B C and △ D B C are congruent. Let's summarize the given information.
Angles ∠ 1 and ∠ 2 are congruent.
Segments BC and AD are perpendicular. Since all right angles are congruent, this means, that angles ∠ A C B and ∠ D C B are congruent.
Let's mark these congruences on the diagram.
We can see that triangle △ A B C and △ D B C have two pairs of corresponding congruent angles.
Since segment B C is a common side of the two triangles that is included between the corresponding angle pairs, we can use the Angle-Side-Angle (ASA) Congruence Postulate to conclude that the two triangles are congruent.
The answer isB.
