Question

D,Eand F are the mid point of the side AB,BC,CA respectively of ∆ABC .Find that ar ∆DEF/ar∆ABC ​

Answer 1

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Answer 2

Answer:

1/4

Step-by-step explanation:

the line joining the midpoints of two sides of a triangle is parallel to third side and half of it.

There fore DE/ AC =  1/2

EF/ AB = 1/2

DF/ BC = 1/2

DE/ AC = EF/ AB = DF/ BC = 1/2

By SSS, ΔABC is similar to ΔEFD

∴ Area of ΔABC / Area of ΔEFD = (DE/AC)²

=( 1/2)²

=1/4

∴ The ratio of Area of ΔABC to that of ΔEFD is 1 : 4