Question
Diagonals of a trapezium $\mathrm{ABCD}$ with $\mathrm{AB} \| \mathrm{DC}$ intersect each other at the point $\mathrm{O}$. If $\mathrm{AB}=2 \mathrm{CD}$, find the ratio of the areas of triangles $\mathrm{AOB}$ and $\mathrm{COD}$.
Step 1
It is given that AB = 2CD. Show more…
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Diagonals AC and BD of a trapezium ABCD with $\mathrm{AB}$ II DC intersect each other at the point $\mathrm{O}$. Using a similarity criterion for two triangles, show that $\frac{\mathrm{OA}}{\mathrm{OC}}=\frac{\mathrm{OB}}{\mathrm{OD}}$.
Triangles
Similarity of Triangles
If $A B C D$ is a trapezium, $A C$ and $B D$ are the diagonals intersecting each other at point $O$. Then $\mathrm{AC}: \mathrm{BD}=$ (1) $\mathrm{AB}: \mathrm{CD}$ (2) $\mathrm{AB}+\mathrm{AD}: \mathrm{DC}+\mathrm{BC}$ (3) $\mathrm{AO}^{2}: \mathrm{OB}^{2}$ (4) $\mathrm{AO}-\mathrm{OC}: \mathrm{OB}-\mathrm{OD}$
$\mathrm{ABCD}$ is a trapezium in which $\mathrm{AB}$ II $\mathrm{DC}$ and its diagonals intersect each other at the point $\mathrm{O} .$ Show that $\frac{\mathrm{AO}}{\mathrm{BO}}=\frac{\mathrm{CO}}{\mathrm{DO}}$
$\quad$ Similar Figures
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