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Question

The diagonals of a parallelogram ABCD intersect at O. A line through O intersects AB at X and DC at Y. Prove that OX = OY. [4 MARKS]


Solution

Diagram : 1 Mark
Concept : 1 Mark
Proof : 2 Marks


Consider ΔAXO and ΔCYO.

AO=CO                          [Diagonals bisect each other]

AOX=COY          [Vertically opposite angles]

AXO=CYO          [Alternate angles]

ΔAXOΔCYO.   [AAS congruency]

OX=OY                        [CPCT]

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