Show that in a right angled triangle, hypotenuse is larger than any of the remaining sides.
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Suppose ABC is a right angled triangle with ∠B=90o. Then AC is the hypotenuse. Observe that ∠BAC<∠B and ∠BCA<∠B. Now the side opposite to ∠BAC is BC and side opposite ∠BCA is AB. Hence by proposition 2, BC < AC and AB < AC