MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Sum of Opposite Angles of a Cyclic Quadrilateral

In the trapez...

Question

In the trapezium ABCD, AD || BC and the diagonals intersect at O. Prove that.

Open in App

Solution

In trapezium ABCD, diagonals AC and BD intersect at O and AD || BC.

In ΔOBC and ΔODA:

Hence, ΔOBC and ΔODA are equiangular.

Suggest Corrections

thumbs-up

0

Similar questions

Q. In trapezium

A B C D

A B ∥ C D

A C

B D

intersect each other at

O

\frac{O A}{O C} = \frac{O D}{O B}

Q. In trapezium

A B C D, A B ∥ D C

and the diagonals intersect at

O

\frac{O D}{O C} =

Q. ABCD is a trapezium such that AB || DC and the diagonals of ABCD intersect at point O. If OD = 5 cm, OB = 8 cm, AC = 26 cm, then the difference between the lengths of OA and OC is equal to

State true or false:

In quadrilateral ABCD,

A D = B C

and the diagonals

A C

B D

intersect at point

O

\frac{O C}{O A} = \frac{O D}{O B} = \frac{1}{3}

, then the quadrilateral

A B C D

is a trapezium.

Q. Diagonals AC and BD of a trapezium ABCD with AB

∥

DC intersect each other at the point O. Using similarity criterion for two triangles, show that

\frac{O A}{O C}

\frac{O B}{O D}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Circles and Quadrilaterals - Theorem 11

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Sum of Opposite Angles of a Cyclic Quadrilateral

Standard IX Mathematics

Join BYJU'S Learning Program

CrossIcon