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

Question:

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

 

Solution:

Let ABCD be a parallelogram and BD be its diagonal.
To prove: ar(∆ABD) = ar(∆CDB)

Proof: 
In ∆ABD and ∆CDBwe have:
AB = CD                    [Opposite sides of a parallelogram]
AD = CB                   [Opposite sides of a parallelogram]​

 BD  = DB                  [Common]

i.e., ∆ABD  CDB           [ SSS criteria]
∴ ar(∆ABD) = ar(∆CDB)

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