Triangles are congruent if any pair of corresponding sides and their included angles are equal in bothtriangles. There are five ways to test that two triangles are congruent. This is one of them
For two Triangles to be congruent by ASA, they have to have two angles which are the same, and their included sides must also be equal(the side between the two angles).
For this scenario:
BC = CD as noted by the single lines through each segment.
∠D in ΔADC =90° and ∠B in ΔEBC = 90°
∠C is common to ΔADC and ΔEBC
Thus,
Both triangles have two angles of the exact same size, with a side length between the two angle of the exact same size.
