ABCD is a trapezium in which AB || DC and its diagonals AC and BD intersect at O. Show that OA/OB = OC/OD .
CBSE Class 10 Maths PYQ · Triangles · Similarity with Quadrilaterals · 3 Marks · July 2023 · Standard
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1343 Marks · July 2023 · Standard
ABCD is a trapezium in which AB $||$DC and its diagonals AC and BD intersect at O. Show that $\frac{OA}{OB} = \frac{OC}{OD}$.
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Draw OE $||$ CD In $\triangle DAB$, OE $||$ AB (since OE $||$ CD and AB $||$ CD) By Basic Proportionality Theorem (BPT): $\frac{DE}{AE} = \frac{DO}{OB}$ In $\triangle ADC$, OE $||$ DC By BPT: $\frac{AE}{DE} = \frac{AO}{OC}$ From the two ratios: $\frac{DO}{OB} = \frac{AO}{OC}$ $\Rightarrow \frac{OA}{OB} = \frac{OC}{OD}$
