Statement Reason
AB * BE = CB * BD Given
CB/BE = AB/BD Cross multiplication property
angle ABC is congruent to angle DBE Vertically opposite angles
Recall, according to the SAS(side angle side) postulate, two triangles are similar iff 2 of their corresponding sides are in proportion and the angle between them is congruent. From statement 2, the ratio of the corresponding sides are in proportion. From statement 3, the angles between the corresponding sides are congruent. Thus, the final statement is
Statement Reason
Triangle ABC is similar to triangle DBE SAS property of similarity