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Standard X

Mathematics

Two Circles Touching Internally and Externally

State true or...

Question

State true or false:

In quadrilateral $A B C D$ , its diagonals $A C$ and $B D$ intersect at point $O$ , such that
$\frac{O C}{O A} = \frac{O D}{O B} = \frac{1}{3}$ , then
$△ O A B \sim △ O C D$

True

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False

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Solution

The correct option is A True
In $△$ s, $O A B$ and $O C D$
$\frac{O C}{O A} = \frac{O D}{O B}$ (Given)
$∠ A O B = ∠ C O D$ (Vertically opposite angles)
Thus, $△ O A B \sim △ O C D$ (SAS rule)

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Similar questions

State true or false:

In quadrilateral ABCD,

A D = B C

and the diagonals

A C

and

B D

intersect at point

O

, such that

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

, then the quadrilateral

A B C D

is a trapezium.

State true or false:

In quadrilateral ABCD, the diagonals AC and BD intersect each at point O. If

A O = 2 C O

and

B O = 2 D O

; Then,

O A \times O D = O B \times O C

In quadrilateral ABCD, its diagonals AC and BD intersect at point O such that $\frac{O C}{O A} = \frac{O D}{O B} = \frac{1}{3}$

If CD =4.5 cm; find the length of AB.

Q. State True or False
In the given fig, diagonals

A C

and

B D

of quadrilateral

A B C D

intersect at

O

such that

O B = O D

. If

A B = C D

, then

a r (D O C)

a r (A O B)

State true or false:

In the given figure, the diagonals

A C

and

B D

intersect at point

O

. If

O B = O D

and

A B ∥ D C

, then

A B C D

is a parallelogram.

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State true or false:In quadrilateral ABCD, its diagonals AC and BD intersect at point O, such thatOCOA=ODOB=13, then△OAB∼△OCD

The correct option is A TrueIn △s, OAB and OCDOCOA=ODOB (Given)∠AOB=∠COD (Vertically opposite angles)Thus, △OAB∼△OCD (SAS rule)

State true or false:

In quadrilateral $A B C D$ , its diagonals $A C$ and $B D$ intersect at point $O$ , such that
$\frac{O C}{O A} = \frac{O D}{O B} = \frac{1}{3}$ , then
$△ O A B \sim △ O C D$

The correct option is A True
In $△$ s, $O A B$ and $O C D$
$\frac{O C}{O A} = \frac{O D}{O B}$ (Given)
$∠ A O B = ∠ C O D$ (Vertically opposite angles)
Thus, $△ O A B \sim △ O C D$ (SAS rule)