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

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles, show that

In Fig. 6.36, and ∠1 = ∠2. Show that Δ PQS ~ Δ TQR.

In Fig. 6.37, if Δ ABE ≅Δ ACD, show that
Δ ADE ~ Δ ABC.

In Fig. 6.38, altitudes AD and CE of Δ ABCintersect each other at the point P. Showthat:

(i) Δ AEP ~ Δ CDP

(ii) Δ ABD ~ Δ CBE

(iii) Δ AEP ~ Δ ADB

(iv) Δ PDC ~ Δ BEC