CBSE Class 10 Maths (Standard) 2023 · Paper 30/C/1 · Question 28

**Basic Proportionality Theorem:** if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. In $△ABC$ with $DE\parallel BC$, $\frac{\text{ar}(△ADE)}{\text{ar}(△BDE)}=\frac{AD}{DB}$ and $\frac{\text{ar}(△ADE)}{\text{ar}(△DEC)}=\frac{AE}{EC}$, and $\text{ar}(△BDE)=\text{ar}(△DEC)$ (same base $DE$, same parallels), so $\frac{AD}{DB}=\frac{AE}{EC}$. Hence proved.