Question

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that

1. ΔAPB ≅ ΔCQD
2. AP = CQ

Answer 1

i. In ΔAPB and ΔCQD,

∠APB = ∠CQD       ...(Each 90°)

AB = CD                ...(Opposite sides of parallelogram ABCD)

∠ABP = ∠CDQ      ...(Alternate interior angles for AB || CD)

∴ ΔAPB ≅ ΔCQD     ...(By AAS congruency)

ii. By using the above result

ΔAPB ≅ ΔCQD, we obtain

AP = CQ          ...(By CPCT)