Here we will prove that if two angles
of a triangle are unequal, the greater angle has the greater side opposite to
Given: In ∆XYZ, ∠XYZ > ∠XZY
To Prove: XZ > XY
1. Let us assume that XZ is not greater
Let XZ = XY
⟹ ∠XYZ = ∠XZY
2. But ∠XYZ ≠ ∠XZY
3. Again, XZ < XY
⟹ ∠XYZ <
4. But ∠XYZ is not less than ∠XZY.
5. Therefore, XZ is neither equal to nor
6. Therefore, XZ > XY. (Proved)
1. Angles opposite to equal sides are
2. Given, ∠XYZ > ∠XZY
3. The greater side of a triangle has the
4. Given that ∠XYZ > ∠XZY.
5. Both the assumptions are leading to contradictions.