Ex 6.3, 3 - Diagonals AC and BD of a trapezium ABCD - Ex 6.3

  1. Chapter 6 Class 10 Triangles
  2. Serial order wise
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Ex 6.3, 3 Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles, show that 𝑂𝐴/𝑂𝐢 = 𝑂𝐡/𝑂𝐷 Given: ABCD is a trapezium with AB II CD and diagonals AB & CD intersecting at O To prove: 𝑂𝐴/𝑂𝐢=𝑂𝐡/𝑂𝐷 Proof: In βˆ† 𝑂𝐴𝐡 and βˆ† 𝑂𝐢𝐷 ∠ 𝐴𝑂𝐡= ∠ 𝐷𝑂𝐢 ∠ 𝐴𝐡𝑂= ∠ 𝐢𝐷𝑂 ∠ 𝐡𝐴𝑂= ∠ 𝑂𝐢𝐷 Ξ” 𝑂𝐴𝐡 ∼ βˆ† 𝑂𝐢𝐷 We know that If 2 triangles are similar , their corresponding sides are in proportion Hence 𝑂𝐴/𝑂𝐢=𝑂𝐡/𝑂𝐷 Hence proved

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