CBSE Class 10 Maths (Basic) 2025 · Paper 430/3/1 · Question 33(a)

**Statement:** If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio. **Proof:** In $△ABC$ with $DE\parallel BC$, join $BE$, $CD$ and draw $EM\perp AB$, $DN\perp AC$. Then $\frac{\text{ar}(△ADE)}{\text{ar}(△BDE)}=\frac{AD}{DB}$ and $\frac{\text{ar}(△ADE)}{\text{ar}(△CDE)}=\frac{AE}{EC}$. Since $△BDE$ and $△CDE$ are on the same base $DE$ between the parallels $DE$ and $BC$, $\text{ar}(△BDE)=\text{ar}(△CDE)$. Therefore $\frac{AD}{DB}=\frac{AE}{EC}$. Hence proved.