Q. 54.4( 39 Votes )

Diagonals AC and

Answer :

Given, trapezium ABCD and diagonals AC and BD intersect each other.


Need to prove


Let us consider Δ AOB and Δ DOC


AOB = DOC (vertically opposite angles)


by alternative interior angles we have


OAB = OCD


OBA = ODC


By AAA similarity we have in two triangles if the angles are equal, then sides opposite to the equal angles are in the same ratio (or proportional) and hence the triangles are similar.


Δ Aob Δ DOC



Hence proved.


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