ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that

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Solution

Draw a line EF through point O, such that

In ΔADC,

By using basic proportionality theorem, we obtain

In ΔABD,

So, by using basic proportionality theorem, we obtain

From equations (1) and (2), we obtain

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Q. Question 9
ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that

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

A B C D

is a trapezium in which

A B | | D C

and its diagonals intersect each other at point

^{'} O^{'}

. Show that

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

Q. The diagonals of a quadrilateral

A B C D

intersects each other at the point

O

such that

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

. Show that

A B C D

is a trapezium.

Q. Question 10
The diagonals of a quadrilateral ABCD intersect each other at the point O such that

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

. Show that ABCD is a trapezium.

Question 9
ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that $\frac{A O}{B O} = \frac{C O}{D O}$ .

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ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that

Draw a line EF through point O, such that In ΔADC, By using basic proportionality theorem, we obtain In ΔABD, So, by using basic proportionality theorem, we obtain From equations (1) and (2), we obtain

Draw a line EF through point O, such that

In ΔADC,

By using basic proportionality theorem, we obtain

In ΔABD,

So, by using basic proportionality theorem, we obtain

From equations (1) and (2), we obtain