Question

In the following figure, BD is parallel to CA, E is mid-point of CA and BD = `1/2`CA
Prove that: ar. ( ΔABC ) = 2 x ar.( ΔDBC )

Answer 1

Here BCED is a parallelogram, Since BD = CE and BD || CE.
ar. ( ΔDBC ) = ar. ( ΔEBC )      ......( Since they have the same base and are between the same parallels )

In ΔABC,
BE is the median,
So, ar. ( ΔEBC ) = `1/2` ar. ( ΔABC )
Now, ar. ( ΔABC ) = ar. ( ΔEBC ) + ar. ( ΔABE)
Also, ar. ( ΔABC ) = 2ar. ( ΔEBC )
⇒ ar. ( ΔABC ) = 2ar. ( ΔDBC )