show that in a right angle triangle, the hypotenuse is the longest side
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In a right angled triangle, the angle opposite To the hypotenuse is 90°, while other two angles are Always less than 90°. As you know that the side opposite to the largest angle is always the largest in a triangle.
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∠A≤∠B<∠C
∠A≤∠B<∠C
,
then the sides are
a≤b<c.
a≤b<c.
On a right triangle, two angles are acute and the third is a right angle.
Hence the side opposite the right angle is the longest side.