Question

In the following figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that:

ΔAEP ∼ ΔCDP

Answer 1

In ΔAEP and ΔCDP,

∠AEP = ∠CDP        ...(Each 90°)

∠APE = ∠CPD        ...(Vertically opposite angles)

Hence, by using AA similarity criterion,

ΔAEP ∼ ΔCDP