Question

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using similarity criterion for two triangles, show that OA/OC = OB/OD.

Answer 1

SOLUTION :  

Given : In trapezium ABCD , AB || DC. OC is the point of intersection of AC and BD.

To prove = OA/OC = OB/OD

Now, in ΔAOB and ΔCOD

∠AOB  = ∠COD    

[Vertically opposite angles]

∠OAB   = ∠OCD    

[alternate interior angles]

Then, ΔAOB∼ΔCOD

Therefore, OA/OC = OB/OD    

[Since, triangles  are Similar ,hence, corresponding Sides will be proportional]

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Answer 2

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