Draw two triangles ABC and DBC on the same base and between the same parallels as shown in the figure with P as the point of intersection of AC and BD. Draw CE || BA and BF || CD such that E and F lie on line AD.
Can you show `ar(DeltaPAB) = ar(DeltaPDC)`
Hint : These triangles are not congruent but have equal areas.

In the figure, ΔABC and ΔABD are two triangles on the same base AB. If line segment CD is bisected by bar(AB) at O, show that ar (DeltaABC) = ar (DeltaABD).

Draw a triangle ABC and mark the midpoints E and F of two sides of triangle. bar(AB) and bar(AC) respectively. Join the point E and F as shown in the figure. Measure EF and the third side BC of the triangle. Also measure angleAEF and angleABC . We find angleAEF = angleABC and bar(EF)=(1)/(2)bar(BC) As these are corresponding angles made by the transversal AB with lines EF and BC, we say EF"||"BC.