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.


Answer :

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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