Question

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 8.13). Show that 

(i) ∆ APB ≅ ∆ CQD 

(ii) AP = CQ

Answer 1

(i) In ∆APB and ∆CQD,

∠APB = CQD (Each 90°)

AB = CD (Opposite sides of parallelogram ABCD) ∠ABP

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

∠∆APB ∠∆CQD (By AAS congruency)

(ii) By using the above result

∆APB ∠∆CQD, we obtain

AP = CQ (By CPCT)