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 $\frac{\mathrm{OA}}{\mathrm{OC}}=\frac{\mathrm{OB}}{\mathrm{OD}}$.

Answer

Related Courses

Geometry

NCERT Class 10 - Math

Chapter 6

Triangles

Section 3

Similarity of Triangles

Discussion

You must be signed in to discuss.

Top Geometry Educators

Watch More Solved Questions in Chapter 6

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Video Transcript

we are going to do problem number three. And this question it is given that deregulation video of Petra Belgium is interesting at Toronto that is seen in the figure. And we need to prove, oh a bio C. This is equals 20 B. By only we have produced similar criteria. Triangles. Okay. And it is given that A. B. Is parallel to B. C. Baby is parallel too busy. Okay. In this case if you see this angle, that angle ah Oh A. B. This is echo strangle O. C. D. Okay. Why? Because of the alternate and daily rangel property and this our panel line a similar to the transfer cell. So we can say that. So that is a straight angle. Oh a bee. This is a equals to trying angle angle O. C. D. Okay. No, this is you do return it interior angle property. No, next year the single that angle O. B. C. And angle O. B. A. These triangles will be brought. Uh this too and will be equal due to the angle property. Okay? Alternate entry angle property. Same property. So this is angle oh, be A. This is equals two angle O. D. C. Same properties there. Now, next is this one angle? Uh It will be is equal strangled. Goc angle A. O. B. This is equals two angle and D. O. C. This is particularly apposite angle. Okay, no, this is the given condition and triangle in our triangle A. Or B. And triangle C. O. D. Or do you see OK. C. O. D. So in this case if you see ah all angles are equal, which means that by a similar secretaria angle angle angle similar create area. Similarly secretaria these two these two and triangle will be similar. Gentlemen, I tell this is criteria. Yeah, we have to choose pennsylvania. No, we will be having triangle A. O. B. This is similar to strangle C. O. D. This is what we got by a similar carrot area. Now, if these two triangular district rangel are similar, which means that, oh, by oc, This should be equals two will be by only. Okay, because similar triangle uh, a similar triangular, the proportional means uh, the two sides to cross burning ships are in proportion. So we will be right here. This is oh A by Oc. This is he calls to OBI by only. So this is what we need to prove. And we have just dropped this. So the answer that shall thank you.

Get More Help with this Textbook