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keshav kumar
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Asked: 2023-03-31T03:19:18+00:00 In:

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD see Figure. Show that (i) ∆ APB ≅ ∆ CQD (ii) AP = CQ

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ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD see Figure. Show that (i) ∆ APB ≅ ∆ CQD (ii) AP = CQ

Find the corresponding angles.
Prove the corresponding sides of congruent triangles
NCERT Books for Session 2022-2023 are based on CBSE Board.
Important NCERT Book, Exercise 7.4, Question no: 10, Page No: 147.

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    1. Best Answer
      ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD see Figure. Show that (i) ∆ APB ≅ ∆ CQD (ii) AP = CQ

      (i) In ΔAPB and ΔCQD,
      ∠APB = ∠CQD [∵ Each 90°]
      ∠ABP = ∠CDQ [∵ Alternate angles]
      AB = CD [∵ Opposite sides of a parallelogram]
      Hence, ΔAPB ≅ ΔCQD [∵ SAS Congruency rule]

      (ii) ΔAPB ≅ ΔCQD [∵ Prove above]
      AP = CQ [∵ CPCT]

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