Question

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 1

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 = 6 cm