- M and N are points on the sides AB and AC respectivelyhat RM = CN. I

1.	- M and N are points on the sides AB and AC respectivelyhat RM = CN. IfZ8-LC then show that MN 11 BC.A.nelie on the same side of BC
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=180°----(1)(Angle Sum Property of triangle) Again In ∆AMN, ∠A + ∠AMN + ∠ ANM =180°---(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

- M and N are points on the sides AB and AC respectivelyhat RM = CN. IfZ8-LC then show that MN 11 BC.A.nelie on the same side of BC

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=180°----(1)(Angle Sum Property of triangle)

Again In ∆AMN,

∠A + ∠AMN + ∠ ANM =180°---(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