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in Parallelograms by (58.8k points)

Show that a diagonal divides a parallelogram into two triangles of equal area.

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We know that

Area of △ ABD = ½ × AB × DL …….. (1)

Area of △ CBD = ½ × CD × BE …….. (2)

Hence, ABCD is a parallelogram.

It can be written as AB || CD and

AB = CD …… (3)

We know that the distance between two parallel lines is constant t,

So we get

DL = BE …….. (4)

Using the equations (1), (2), (3) and (4)

We get

Area of △ ABD = ½ × AB × DL

It can be written as

Area of △ ABD = ½ × CD × BE

So we get

Area of △ ABD = Area of △ CBD

Therefore, it is proved that a diagonal divides a parallelogram into two triangles of equal area.

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