# Problem Set 2

Recall that the Pythagorean Theorem is that the sum of the squares of the two legs of a right triangles is equal to the square of the hypotenuse, or for legs,

*a*and*b,*and hypotenuse,*c,*of some right triangle. Explore this idea in two dimensions.## 1. Use the Pythagorean Theorem to find the hypotenuse for the following set of legs, and show that it works, geometrically.

a) 3 and 4 b) 5 and 12 c) 7 and 24 d) 8 and 8

## Geogebra Applet for Problem 1

## 2. Find another pythagorean triple based off one of the above right triangles. Show that it is a Pythagorean Triple.

## Geogebra Applet for Problem 2

## 3. Is there a way to calculate a pythagorean triple?

a) For x = 7, find and . Check to see if these three values make a right triangle. b) For x = 8, find and . Check to see if these three values make a right triangle. c) Do you have any conjectures? Test it. Prove it. This problem was “brought” to you by Plato (plus.math.org).