Question

D, G are points on the side AB of ∆ ABC. E and F are points on the sides AC and BC respectively such that DE // BC, EF // AB and FG // CA. Then D, E, F, G are the
consecutive vertices of a quadrilateral

A) always
B) only if (AD/AB) > (1/2)
C) only if (AD/AB) = (1/2)
D) only if (AD/AB) < (1/2)
E) none of these

Answer 1

Answer:

Answer is (D) only if (AD/AB) < (1/2)

Step-by-step explanation:

If AD/AB > 1/2 we don't get a quadrilateral because GF intersects with DE;

If AD/AB = 1/2 so D≡G and we don't get equilateral again.

If AD/AB < 1/2 so it's valid.

Now, we see that A) and E) are not relevant.