Question

in the adjoining figure BD||CA,E is the mid point of CA and BD=1/2CA.prove that ar(ABC)=2ar(DBC)​

Answer 1

Step-by-step explanation:

Answer 2

Area of ΔABC = 2  Area of ΔDBC In the adjoining figure BD||CA,E is the mid point of CA and BD=1/2CA

Step-by-step explanation:

E is the mid point of CA

=> CE = CA/2

BD = CA/2

=> BD = CE

BD ║ CA => BD ║CE

BD = CE &  BD ║CE

=> BCED is a parallelogram

Diagonal of parallelogram divided it into two equal area traingle

=> Area of ΔDBE = Area of ΔCBE = (1/2) Area of  BCED

Area of ΔDBC = Area of ΔEBC = (1/2) Area of  BCED

=>  Area of ΔCBE =  Area of ΔDBC

in ΔABC  , BE is the median

Hence

Area of ΔCBE = (1/2) Area of ΔABC

=> Area of ΔDBC  = (1/2) Area of ΔABC

=> Area of ΔABC = 2  Area of ΔDBC

QED

proved

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