# The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO = CO/DO. Show that ABCD is a trapezium

**Solution:**

As we know If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

In quadrilateral ABCD

Diagonals AC, BD intersect at ‘O’

Draw OE||AB

In ΔABC

OE || AB

⇒ OA/OC = BE/CE (Basic Proportionality Theorem) (1)

But-OA/OB = OC/OD (given)

⇒ OA/OC = OB/OD.............. (2)

From (1) and (2)

OB/OD = BE/CE

In ΔBCD

OB/OD = BE/CE

OE || CD

OE || AB and OE || CD

⇒ AB || CD

⇒ ABCD is a trapezium

**Video Solution:**

## The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO = CO/DO. Show that ABCD is a trapezium

### Class 10 Maths NCERT Solutions - Chapter 6 Exercise 6.2 Question 10:

The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO = CO/DO. Show that ABCD is a trapezium

The diagonals of a quadrilateral ABCD intersect each other at the point such that AO/BO = CO/DO. Hence it is proved that ABCD is a trapezium