O is a point of intersection of the diagonals AC and BD of a trapezium ABCD with AB || DC.Through o,a line segment PG is drawn parallel to AB meeting AD in P and BC in Q.Prove that PO = QO

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- Sep 18th 2010, 10:12 AManshulbshahSimilarity of Triangles
O is a point of intersection of the diagonals AC and BD of a trapezium ABCD with AB || DC.Through o,a line segment PG is drawn parallel to AB meeting AD in P and BC in Q.Prove that PO = QO

- Sep 18th 2010, 11:20 AMArchie Meade
Hello anshulbshah,

If you draw your trapezium,

you will find that the areas of triangles BDC and ADC are equal, as the have the same bases and perpendicular heights.

Then use the fact that triangle APO is a reduced version of ADC

and triangle BOQ is a reduced version of BDC.

It follows that since their areas are equal and they have the same perpendicular heights,

then their bases PO and OQ must be equal.