Q-12. Prove that angles opposite to equal sides of an isosceles triang

1.	Q-12. Prove that angles opposite to equal sides of an isosceles triangle are equal.
Answer» Given:\xa0In the isosceles ∆XYZ, XY = XZ.To prove\xa0∠XYZ = ∠XZY.Construction:\xa0Draw a line XM such that it bisects ∠YXZ and meets the side YZ at M.Proof:\tStatement1. In ∆XYM and ∆XZM,(i) XY = XZ(ii) XM = XM(iii) ∠YXM = ∠ZXM\xa02. ∆XYM ≅ ∆XZM3. ∠XYZ = ∠XZY. (Proved)Reason1.(i) Given.(ii) Common side.(iii) XM bisects ∠YXZ.\xa02. By SAS criterion.3. CPCTC.\t

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