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Question

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Which of the following should be true?


  1. ΔAPBΔCQD

  2. Cannot be determined
  3. AB = BP
  4. CQ = PQ


Solution

The correct option is A

ΔAPBΔCQD


InΔAPBΔCQD
APB=CQD (Each90)
AB = CD (Opposite sides of parallelogram ABCD)
ABP=CDQ (Alternate interior angles for AB || CD)
ΔAPBΔCQD (By AAS congruency)
 

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