Geometry for elementary school/Pythagorean theorem

Write about Pythagorean_theorem and its use to prove that $\sqrt{0.5}$ is an irrational number.

Introduction

In this chapter, we will discuss the Pythagorean theorem. It is used the find the side lengths of right triangles. It says:

In any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (i.e. the two sides other than the hypotenuse).

This means that if $\mathrm{△}ABC$ is a right triangle, the the length of the hypotenuse, c, squared eqauls the sum of a squared plus b squared. Or:

$a^2+b^2=c^2$

Here's an example:

In a right-angled triangle, a=5cm and b=7cm, so what is c?

$a^2+b^2=c^2$

$c=\sqrt{5^2+7^2}$

$c=\sqrt{25+49}$

$c=\sqrt{74}$

$c=8.6$

If c is not larger than a or b, your answer is incorrect.