Q5 of 42 Page 210

Diagonals AC and BD of a trapezium ABCD with AB||DC intersect each other at the point ‘O’. Using the criterion of similarity for two triangles, show that

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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