E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that △ ABE ~ △ CFB.

In the given figure, altitudes AD and CE of ∆ ABC intersect each other at the point P. Show that:

(i) ∆ AEP ~ ∆ CDP

(ii) ∆ ABD ~ ∆ CBE

(iii) ∆ AEP ~ ∆ ADB

(iv) ∆ PDC ~ ∆ BEC

S and T are points on sides PR and QR of △ PQR such that ∠P = ∠RTS. Show that △ RPQ ~ △ RTS.