Last updated at Dec. 8, 2016 by Teachoo

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Ex 9.3, 16 In figure, ar(DRC) = ar(DPC) and ar(BDP) = ar(ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums. Given: ar(DRC) = ar(DPC) & ar(BDP) = ar(ARC) To prove: ABCD & DCPR are trapeziums Proof: Given ar(DRC) = ar(DPC) So, ΔDPC and ΔDRC lie on the same base DC and are equal in area & They lie between DC & PR Hence DC ∥ PR In DCPR, one pair of opposite sides of quadrilateral DCPR are parallel Hence, DCPR is a trapezium . Now, given that ar(BDP) = ar(ARC) & ar(DPC) = ar(DRC) Subtracting(1) & (2),i.e., (1) – (2) ar(BDP) – ar(DPC) = ar(ARC) – ar(DRC) ar(BDC) = ar(ADC) Now, ΔADC and ΔBDC lie on the same base DC and are equal in area & They lie between lines DC & AB ∴ DC ∥ AB Since one pair of opposite sides of quadrilateral ABCD are parallel Hence, ABCD is a trapezium .

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.