Q. 2

# If diagonals AC and BD of trapezium ABCD with AB || CD intersect each other at 0 and AB= 18 cm, DC = 30 cm, OB =y cm, OD= 10 cm, find y.

Given: ABCD is a trapezium with AB || CD

and diagonals AB and CD intersecting at O

To find: y

Firstly, we prove that OAB ~ ODC

Let OAB and ODC

AOB = COD [vertically opposite angles]

OBA = ODC [AB || CD with BD as transversal.

alternate angles are equal]

OAB = OCD [AB || CD with BD as transversal.

alternate angles are equal]

OAB ~ ODC [by AAA similarity]

Since triangles are similar. Hence corresponding sides are proportional.

y = 6cm

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