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

  1. Chapter 6 Class 10 Triangles
  2. Serial order wise
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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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