Answer
Angle A corresponds to Angle C.
Angle E corresponds to Angle D.
Angle ABE corresponds to Angle CBD.
Side AE corresponds to Side CD.
Side EB corresponds to Side DB.
Side AB corresponds to Side BC.
Work Step by Step
Let's remember that for triangle ABE and triangle CBD to be similar two conditions must be met:
1) The corresponding angles have the same measure. (These angles are determined by the small arcs at the angles)
2) The corresponding sides are proportional.
As both triangles share Angle B,and the segments AE and CD are parallel, we could see the pair of triangles as angle pairs of parallel lines intersected by the transversal AC and the transversal ED which meet at point B.
In this case, angles A and C are alternate interior angles which make their angle measures equal. Angles E and D are also alternate interior angles, with equal angle measures.
To name the angle B in both triangles, just name the three vertices that make up the angle, with the angle you are referring to in the middle. Therefore, angle ABE corresponds to angle CBD.
Because of the relationship between the angles, the sides correspond as the ratio between their angles is proportional.
