ABCD is a trapezium in which AB || DC and its diagonals intersect at O. Show that

ABCD is a parallelogram on whose side BC a point P lies. It DP and AB are produced ahead then they meet at L. Then prove that

(i) (ii)

On side AB of ΔABC two points D and E lie such that AD = BE. If DP || BC and EQ || AC then prove that PQ || AB.

If D and E are points lying on sides AB and AC respectively of ΔABC such that BD = CE. Then prove that ΔABC is an isosceles triangle.

In two triangles ABC and PQR Name two angles of two triangles which must be equal so that these triangles may be similar. Give reason also for your answer.