How is the hypotenuse the longest side of any right triangle? I see that the hypotenuse of a right triangle is opposite the right angle, but how is it always the longest side?  I also know that it connects to endpoints of other sides.  Please help me out with this!  I'm really wanting to know this surprising thing.  Here's an example of a right triangle:
This is an isosceles right triangle because sides a and b (the height and the base) are the same lengths with two of the angles being 45 degrees adding up to a total with the right angle of 180 degrees (all triangles have angles that add up to 180 degrees).  I just want to know from this triangle or any other right triangles why the hypotenuse is the longest side.  You'll really be helping me out.

Let $a$ be the hypotenuse and $b,c$ the others sides, then by Pythagorean Theorem
$$a^2=b^2+c^2.$$
Then
$$a^2>b^2,\quad a^2>c^2.$$
Therefore
$$a>b\quad a>c.$$
