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The diagonals AC and BD of quadrilateral ABCD bisect each other at O. How many pairs of opposite triangles (△AOB with △COD, and △AOD with △COB) are congruent?

Class 9Conditions for a ParallelogramGeometry — Quadrilaterals
  • ABoth pairs
  • BOnly one pair
  • CNone
  • DIt depends on the lengths of the diagonals

Step-by-Step Solution

OA = OC, OB = OD and the vertically opposite angles at O are equal, so △AOB ≅ △COD and △AOD ≅ △COB (SAS). Both pairs are congruent, which gives AB = CD and AD = CB — so ABCD is a parallelogram.
Answer: A) Both pairs

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