Question

3.
Show that the diagonals of a parallelogram divide
it into four triangles of equal area.​

Answer 1

AnswEr :

Let ABCD is an parallelogram with diagonals AC & BD intersecting at point O.

We know that :

Diagonals of parallelogram bisect each other at point of intersection.

=> OA = OC & OB = OD

Also, Median of Triangle divide it into two equal parts.

Now , In∆ ABC BO is the median

=> ar (∆OAB) = ar (∆OBC) __________eq(1)

In ∆ BCD , CO is median

=> ar(∆OBC) = ar(∆OCD) ___________eq (2)

In ∆ACD, DO is median

=> ar(∆OCD ) = ar(∆OAD) ___________eq(3)

From eqn 1,2 & 3

ar(∆OAB) =ar(∆OBC) =ar(∆OCD) = ar(∆OAD)

Hence Proved