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 $\mathrm{COD}$.

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Geometry

NCERT Class 10 - Math

Chapter 6

Triangles

Section 4

Criteria for Similarity of Triangles

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Problem 1

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Problem 4

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Problem 6

Problem 7

Problem 8

Problem 9

Video Transcript

We have a problem # two. And this it is given the diagonals of trumpism. A. B. C. D. Okay A. B. C. D. With a BD paddle. A. B. Pallet to D. C. Intersect each other at all. And one more Condition is being given. One more thing has been given that may be equal to two CD. To find the ratio video triangle will be, it will be M. C. O. D. So let's draw a trapeze Ium to busy um A. B. And C. D. Where it is given that A. B paddle to D. C. A. Be parallel to D. C. These two are parallel and these are the diagonals. This is all this is all A. B. Equal to two Cd. It has been given that A. B. Equal to two C. D. Okay to find the ratio of the area of the triangle U. B. And you'll see now. Okay we can say that strangle A. O. B. In triangle A. O. B. And strangle C. O. D. Angle. We can say if this is angle of one, this is an angle to And this is Angle three and this is angle four. We can say that angle of unequal to angle to an angle three equal to angle for these are the alternate angles and these are particularly opposed angles. So triangle A. O. B. Will be similar to triangle C. O. D. By angle angle criteria. Okay, so these are the similar triangles. So we can say that area of triangle A. Or B. By area of a triangle. C. O. D. C. O. Day will be equal to A. B. S. Squad by cD esquire because this will be a squad of the ratios of their sites. Okay now A. B. Is given A to C. D. So to C. D squared by CD square. So four C. D. Squared by city square 24. eight years are in the ratio of four is 2 one. Thank you so much.

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