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The diagonals of parallelogram ABCD meet at O.
Through O a line is drawn meeting AB at E and DC at F.
Using the fact that O bisects both diagonals, what can be said about OE and OF?

Class 9Conditions for a ParallelogramGeometry — Quadrilaterals
  • AOE = OF
  • BOE = 2 OF
  • COE + OF = AB
  • DOE is perpendicular to OF

Step-by-Step Solution

In triangles OEB and OFD, OB = OD (O bisects BD), vertically opposite angles at O are equal, and angle OBE = angle ODF (alternate angles, AB parallel DC). By ASA the triangles are congruent, so OE = OF.
Answer: A) OE = OF

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