D- E- F are the midpoints of the sides BC- CA- AB respectively of - ABC- then the ratio area - DEF - area - ABC is equal to

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D, E, F are t...

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$D, E, F$ are the midpoints of the sides $B C, C A, A B$ respectively of $Δ A B C$ , then the ratio area $Δ D E F$ : area $Δ A B C$ is equal to

1 : 2

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1 : 3

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2 : 3

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1 : 4

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Solution

The correct option is D $1 : 4$
The four triangle formed by joining the midpoints of the sides of a triangle respectively are congruent to each other. Hence, area of each triangle is equal .
Therefore, $A r . Δ D E F : A r . Δ A B C$ $= 1 : 4$

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D,E,F are the midpoints of the sides BC,CA,AB respectively of ΔABC, then the ratio area ΔDEF : area ΔABC is equal to

The correct option is D 1:4The four triangle formed by joining the midpoints of the sides of a triangle respectively are congruent to each other. Hence, area of each triangle is equal .Therefore, Ar.ΔDEF:Ar.ΔABC =1:4

$D, E, F$ are the midpoints of the sides $B C, C A, A B$ respectively of $Δ A B C$ , then the ratio area $Δ D E F$ : area $Δ A B C$ is equal to

The correct option is D $1 : 4$
The four triangle formed by joining the midpoints of the sides of a triangle respectively are congruent to each other. Hence, area of each triangle is equal .
Therefore, $A r . Δ D E F : A r . Δ A B C$ $= 1 : 4$