Q. 104.4( 335 Votes )

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 8.21). Show that



(i) Δ APB Δ CQD

(ii) AP = CQ

Answer :

(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

CPCT: Corresponding parts of congruent triangles are congruent

AP = CQ (By CPCT)

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