Question

D, E, F are mid points of sides BC, CA, AB of triangleABC. Find the ratio of areas of triangleDEF
and triangleABC.​

Answer 1

Answer:

1/4 I think this the answer but not sure about this answer

Answer 2

Answer:

By using mid theorem i.e., the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

∴ DF || BC And DF = 1/2 BC ⟹ DF = BE Since, the opposite sides of the quadrilateral are parallel and equal.

Hence, BDFE is a parallelogram Similarly, DFCE is a parallelogram.

Now, in ∆ABC and ∆EFD ∠ABC= ∠EFD ∠BCA = ∠EDF

By AA similarity criterion, ∆ABC ~ ∆EFD If two triangles are similar, then the ratio of their areas is equal to the squares of their corresponding sides .

Hence, the ratio of the areas of ∆DEF and ∆ABC is 1 :4

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