Question

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.

Answer 1

- Let $\triangle ABC$ be a triangle and a line $DE \parallel BC$ intersecting $AB$ at $E$ and $AC$ at $F$. - By the basic proportionality theorem (Thales' theorem), we know that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

$$\frac{AE}{EB} = \frac{AF}{FC}$$

- This is the required proof.