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The diagonals of a quadrilateral ABCD …

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

Posted by Arijit Ghosh 4 years, 1 month ago

CBSE > Class 10 > Mathematics

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Ayush Singh 4 years, 1 month ago

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Bharti Yadav 4 years, 1 month ago

Given: The diagonals of a quadrilateral ABCD intersect each other at the point O such that BOAO=DOCO i.e., COAO=DOBO To Prove: ABCD is a trapezium Construction: Draw OE∥DC such that E lies on BC. Proof: In △BDC, By Basic Proportionality Theorem, ODBO=ECBE............(1) But, COAO=DOBO (Given) .........(2) ∴ From (1) and (2) COAO=ECBE Hence, By Converse of Basic Proportionality Theorem, OE∥AB Now Since, AB∥OE∥DC ∴ AB∥DC Hence, ABCD is a trapezium.

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CBSE > Class 10 > Mathematics