Question

In the figure, given below, straight lines AB and CD intersect at P; and AC || BD. Prove that: ΔAPC and ΔBPD are similar.

Answer 1

In ΔAPC and ΔBPD,

∠APC = ∠BPD  ...(Vertically opposite angles)

∠ACP = ∠BDP  ...(Alternate angles since AC || BD)

ΔAPC ∼ ΔBPD  ...(AA criterion for similarity)