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Ex 6.2, 10 - Diagonals of quadrilateral ABCD intersect each - Ex 6.2

Ex 6.2, 10 - Chapter 6 Class 10 Triangles - Part 2
Ex 6.2, 10 - Chapter 6 Class 10 Triangles - Part 3

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Ex 6.2, 10 The diagonals of a quadrilateral ABCD intersect each other at the point O such that 𝐴𝑂/𝐡𝑂 = 𝐢𝑂/𝐷𝑂 . Show that ABCD is a trapezium Given: ABCD is a quadrilateral where diagonals AC & BD intersect at O & 𝐴𝑂/𝐡𝑂=𝐢𝑂/𝐷𝑂 To prove: ABCD is a trapezium Construction: Let us draw a line EF II AB passing through point O. Proof: Given 𝐴𝑂/𝐡𝑂=𝐢𝑂/𝐷𝑂 β‡’ 𝐴𝑂/𝐢𝑂=𝐡𝑂/𝐷𝑂 Now, in βˆ† 𝐴𝐷𝐡 EO II AB 𝐴𝐸/𝐷𝐸=𝐡𝑂/𝐷𝑂 β‡’ 𝐴𝐸/𝐷𝐸=𝐴𝑂/𝐢𝑂 Thus in Ξ” ADC, Line EO divides the triangle in the same ratio ∴ EO II DC Now, EO II DC But, we know that EO II AB β‡’ EO II AB II DC β‡’ AB II DC Hence, one pair of opposite sides of quadrilateral ABCD are parallel Therefore ABCD is a trapezium . Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.