Why is the hypotenuse always longer than the legs?

1 Answer
Dec 28, 2015

Hypotenuse is located opposite to a bigger angle (the right angle measured at #90^o#) while other two legs (catheti) are located opposite to smaller acute angles.
See details below.


In any triangle sides, opposite to congruent angles, are congruent.
A side, opposite to a bigger angle, is bigger than a side that lies opposite to a smaller angle.

For a proof of these statements I can refer you to Unizor, menu items Geometry - Triangles - Sides & Angles.

The largest angle in a right triangle is the right angle, therefore, opposite to it lies the longest side - hypotenuse.