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Last updated at May 29, 2018 by Teachoo

Transcript

Example 6 In figure, OA . OB = OC . OD. Show that ∠ A = ∠ C and ∠ B = ∠ D. Given: OA × OB = OC × OD To Prove: ∠ A = ∠ C and ∠ B = ∠ D Proof:- OA . OB = OC . OD 𝑂𝐴/𝑂𝐶=𝑂𝐷/𝑂𝐵 In Δ AOD & Δ COB 𝑂𝐴/𝑂𝐶=𝑂𝐷/𝑂𝐵 ∠ AOD = ∠ COB Using SAS similarity criterion So, ∆ 𝐴𝑂𝐷 ~ ∆ 𝐶𝑂𝐵 We know that if two triangles are similar so, their corresponding angles are equal So, ∠ A = ∠ C & ∠ D = ∠ B Hence proved

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.