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Let the diagonals AC and BD of parallelogram ABCD meet at O.
A line through O meets AB at X and DC at Y.
What can you conclude about OX and OY?

Class 9Properties of a ParallelogramGeometry — Quadrilaterals
  • AOX = OY
  • BOX = 2 OY
  • COX is perpendicular to OY
  • DOX = AB

Step-by-Step Solution

O is the centre of symmetry; triangles OXA and OYC are congruent (ASA using AO = CO, vertically opposite angles, alternate angles), so OX = OY.
Answer: A) OX = OY

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