D, E and F are the mid-points of BC, CA and AB respectively in ΔABC. Prove that the area of ؈BDEF=1/2area of ΔABC.
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Answer:
2Area of ΔDEF = Area of ΔABC/2
Step-by-step explanation:
D, E and F are the mid-points of BC, CA and AB respectively in ΔABC
=> DE = AB/2
& EF = BC/2
& DF = CA/2
=> ΔABC ≅ ΔDEF
Ratio of sides = 2
Area of similar triangles is in ratio of square of ratio of their sides
=> Area of ΔABC = 2² Area of ΔDEF
=> 2Area of ΔDEF = Area of ΔABC/2
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