Question

If PQ||RS,prove ∆POQ~∆ROS.Figure in the attachment!!​

Answer 1

angle poq = angle ros

and angle qpo= angle rso. .as they are interior opposite angles

by AA similarity this two triangles are similar..

Answer 2

Consider the ∆POQ and ∆ROS angle POQ=angle ROS(opposite sides are equal)

angle OQP=angle ORS (PQparallel to RS)

angle OPQ=angle OSR (PQparallel to RS)

therefore ∆POQ~∆ROS