Question

5. D, E and F are respectively the mid-points of sides AB, BC and CA of A ABC. Find the ratio of the areas of A DEF and A ABC.​

Answer 1

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