Question

In trapezoid ABCD, AB||CD and AC and BD intersect at point P.If AB=10cm ,CD=4cm ,AC=7cm ,BD=10.5cm.Find PA,PB,PC and,PD?​

Answer 1

Answer:

In △ APB and △ CPD,

∠APB=∠CPD (Vertically opposite angles)

∠ABP=∠CDP (Alternate angles of parallel sides AB and CD)

∠BAP=∠DCP (Alternate angles of parallel sides AB and CD)

Hence, △APB∼△CPD (AAA rule)

Thus, PCPA=PDPB

PA×PD=PB×PC