Question 7

$$D$$, $$E$$, $$F$$ are the mid points of the sides $$BC$$, $$CA$$ and $$AB$$ of a triangle $$ABC$$.

Solution

By the mid-point theorem, the segment joining the mid points of two sides is parallel to the third side and half of it, so $$DE \parallel AB$$ and $$EF = \frac{1}{2}BC$$. The four small triangles formed are congruent, so area of $$\triangle DEF = \frac{1}{4}$$ area of $$\triangle ABC$$, not $$\frac{1}{3}$$. Hence options a, b and d are correct.

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