Q2 of 95 Page 6

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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