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The diagonals of a quadrilateral ABCD …

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The diagonals of a quadrilateral ABCD intersect each other at point at o such that AO/BO=CO/DO. Show that ABCD is a trapezium.

Posted by Shanaya Rawat 6 years, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

Qwerty G 6 years, 2 months ago

Given- ABCD is a trapezium with AB//CD and the diagonals AC and BD intersect at O. To prove- OA/OC = OB/OD Proof- In the figure consider the Δ OAB and OCD Angle DOC = Angle AOB ( vertically opp. Angles are equal) Since AB // DC Angle DOC =Angle OAB (alternative angles are equal) therefore AA corollary of similar triangles Therefore Δ OAB ~ Δ OCB when the 2 Δ are similar ,the side are proportionally. OA/OC =OB/OD . Hence proved

1Thank You

Aadya Singh ? 6 years, 2 months ago

Firstly, Draw a line parallel to AB and CD and then prove it by using Thales theorem.

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CBSE > Class 10 > Mathematics