The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/OC = BO/OD . Show that…
CBSE Class 10 Maths PYQ · Triangles · Similarity with Triangles · 2 Marks · March 2026 · Standard
Solve it yourself first — then press ↓ or tap Show Solution. Use ←→ for previous / next question.
962 Marks · March 2026 · Standard
The diagonals of a quadrilateral ABCD intersect each other at the point O such that $\frac{AO}{OC} = \frac{BO}{OD}$. Show that quadrilateral ABCD is a trapezium.
Show SolutionHide Solution↓
Correct figure (1/2 Mark) $\triangle AOB \sim \triangle COD$ (1 Mark) $\therefore \angle OAB = \angle OCD$ As alternate angles are equal, so DC $\|\|$ AB (1/2 Mark) Therefore, ABCD is a trapezium. Alternate solution: Correct figure. (1/2 Mark) Draw EO $\|\|$ AB to intersect AD at E. In $\triangle ABD$, EO $\|\|$ AB $\therefore \frac{AE}{ED} = \frac{BO}{OD}$ (1/2 Mark) Given, $\frac{AO}{OC} = \frac{BO}{OD}$ So, $\frac{AE}{ED} = \frac{AO}{OC}$ (1/2 Mark) $\therefore EO\|\| DC$ So, DC $\|\|$ AB (1/2 Mark) Therefore, ABCD is a trapezium.
