Question

Abcd is a trapezium in which ab parallel to dc and it's diagonals intersects each other at the pot o show that ao/bo =co/do

Answer 1

Hoping my answer is correct

Answer 2

Question :

ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O.Show AO/BO = CO/DO

Given :

ABCD is a trapezium where AB||DC and diagonals AC and BD intersect each other at O.

To prove :

$\sf{\dfrac{AO}{BO}=\dfrac{CO}{DO}}$

Solution :

From the point O,draw a line XO touching AD at X,in such a way that,XO||DC||AB

In triangle ADC,we have OX||DC

Therefore, by using basic proportionality theorem

$\sf{\frac{AE}{XD} = \frac{AO}{CO}}$--(i)

Now,in triangle ABD OX||AB

By using basic proportionality theorem

$\sf{\frac{DX}{XA} = \frac{DO}{BO}}$--(ii)

From equation (i) and (ii), we get,

$\sf{\frac{AO}{CO} = \frac{BO}{DO}}$

$\sf{→\frac{AO}{BO} = \frac{CO}{DO}}$

Hence Proved.

Additional Information :

Basic proportionality theorem :

If a line is drawn parallel to one side of the triangle , Then the other sides are divided in the same ratio.

Here, We prove that

In trapezium ABCD , AO/BO = CO/DO

Using the Basic proportionality theorem.

We constructed OX || AB and proceeded with the problem.

Check out the attachment for detailed explanation.