Question

Fig. 8.20 D P 10. ABCD is a parallelograin and AP and CQ are perpendiculars from vertices A and C on diagonal BD (cee Fig. 8.21). Show that (1) A APBE ACQD (ii) AP=CQ is at А B. Fig. 8.21
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Answer 1

Answer:

Given: ABCD is a parallelogram and AP ⊥ DB, CQ ⊥ DB

(i) In ΔAPB and ΔCQD,

∠APB = ∠CQD (Each 90°)

AB = CD (Opposite sides of parallelogram ABCD)

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

∴ ΔAPB ≅ ΔCQD (By AAS congruency)

(ii) By using the result ΔAPB ≅ ΔCQD., we obtain AP = CQ (By CPCT)

Answer 2

Answer:

Given: ABCD is a parallelogram and AP ⊥ DB, CQ ⊥ DB

(i) In ΔAPB and ΔCQD,

∠APB = ∠CQD (Each 90°)

AB = CD (Opposite sides of parallelogram ABCD)

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

∴ ΔAPB ≅ ΔCQD (By AAS congruency)

(ii) By using the result ΔAPB ≅ ΔCQD., we obtain AP = CQ (By CPCT)