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Show that the diagonals of a parallel...

Show that the diagonals of a parallelogram divide it into four triangles of equal area.

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Let E, E, F be the midpoints of BC, CA and AB.
Then, DE `=(1)/(2)AB=AF, DF=(1)/(2)AC = AE.`
`therefore triangle AFE ~= triangle DEF " " [ because AF = DF, AE = DF, FE = EF].`
Similarly, `triangle DEF ~= triangle FBD and triangle DEF ~= triangle EDC. `
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