Which theorem do we use in proving that hypotenuse is the longest side

1.	Which theorem do we use in proving that hypotenuse is the longest side of a right angled triangle?
Answer» In ∆ABC, ∠ABC = 90° ∴ ∠BAC < 90° and ∠ACB < 90° [Given] ∴ ∠ABC > ∠BAC and ∠ABC > ∠ACB ∴ AC > BC and AC > AB [Side opposite to greater angle is greater] ∴ Hypotenuse is the longest side in right angled triangle. We use theorem, If two angles of a triangle are not equal, then the side opposite to the greater angle is greater than the side opposite to the smaller angle.

Which theorem do we use in proving that hypotenuse is the longest side of a right angled triangle?

Answer»

In ∆ABC,

∠ABC = 90°

∴ ∠BAC < 90° and ∠ACB < 90° [Given]

∴ ∠ABC > ∠BAC and ∠ABC > ∠ACB

∴ AC > BC and AC > AB [Side opposite to greater angle is greater]

∴ Hypotenuse is the longest side in right angled triangle.

We use theorem, If two angles of a triangle are not equal, then the side opposite to the greater angle is greater than the side opposite to the smaller angle.

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Which theorem do we use in proving that hypotenuse is the longest side of a right angled triangle?

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