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A8C. M and N are points on the sides AB and AC nepectivelssch that BM CN IfB 2C then show that MN BC |
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Answer» AB = AC (Sides opposite to equal angle are equal)Subtracting BM from both sides, we getAB – BM = AC – BM AB – BM = AC – CN (∵BM =CN)AM =AN∴∠AMN =∠ ANM (Angles opposite to equal sides are equal) Now, in ∆ABC,∠A+ ∠B+ ∠C=1800----(1)(Angle Sum Property of triangle)Again In ∆AMN,∠A + ∠AMN + ∠ ANM =1800----(2)(Angle Sum Property of triangle)From (1) and (2), we get∠B+ ∠C= ∠ AMN + ∠ ANM 2∠B = 2∠ AMN∠B = ∠ AMN Since, ∠B and ∠ AMN are corresponding angles. ∴ MN ‖ BC |
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