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प्रश्न
ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that
- ΔAPB ≅ ΔCQD
- AP = CQ
उत्तर
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)
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