Ex 6.2, 9 - ABCD is a trapezium in which AB || DC and - Ex 6.2

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Ex 6.2 ,9 ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that 𝐴𝑂/𝐡𝑂 = 𝐢𝑂/𝐷𝑂 Given: ABCD is a trapezium where AB II DC & diagonals AC & BD intersect at O To prove: 𝐴𝑂/𝐡𝑂=𝐢𝑂/𝐷𝑂 Construction: Let us draw a line EF II AB II DC passing through point O. Proof: Now , in βˆ† 𝐴𝐷𝐢 EO II DC So, 𝐴𝐸/𝐷𝐸=𝐴𝑂/𝐢𝑂 Similarly , In Ξ” DBA EO II AB 𝐴𝐸/𝐷𝐸=𝐡𝑂/𝐷𝑂 From (1) & (2) 𝐴𝑂/𝐢𝑂=𝐡𝑂/𝐷𝑂 𝐴𝑂/𝐡𝑂=𝐢𝑂/𝐷𝑂 Hence proved

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