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

**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. Proof: draw $OE\parallel AB$ meeting $AD$ at $E$. In $△DAB$, BPT gives $\frac{DE}{EA}=\frac{DO}{OB}$; the given ratio gives $\frac{DO}{BO}=\frac{CO}{AO}$, so $\frac{DE}{EA}=\frac{CO}{OA}$. By the converse of BPT in $△DAC$, $EO\parallel DC$. Since $OE\parallel AB$ and $OE\parallel DC$, $AB\parallel DC$, so ABCD is a trapezium. Hence proved.