# Pythagorean Theorem Calculator

... then the biggest square has the exact same area as the other two squares put together! It is called "Pythagoras" Theorem" & can be written in one short equation:

a2 + b2 = c2 Note:

c
is the longest side of the triangle a and b are the other two sides

## Definition

The longest side of the triangle is called the "hypotenuse", so the formal definition is:

In a right angled triangle:the square of the hypotenuse is equal tothe sum of the squares of the other two sides.

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### Example: A "3, 4, 5" triangle has a right angle in it. Let"s check if the areas are the same: 32 + 42 = 52 Calculating this becomes: 9 + 16 = 25 It works ... like Magic! ## Why Is This Useful?

If we know the lengths of two sides of a right angled triangle, we can find the length of the third side. (But remember it only works on right angled triangles!)

## How Do I Use it?

Write it down as an equation: a2 + b2 = c2

### Example: Solve this triangle  Read Builder"s Mathematics lớn see practical uses for this.

Also read about Squares and Square Roots to lớn find out why √169 = 13

### Example: Solve sầu this triangle. ### Example: What is the diagonal distance across a square of size 1? It works the other way around, too: when the three sides of a triangle make a2 + b2 = c2, then the triangle is right angled.

### Example: Does this triangle have a Right Angle?

Does a2 + b2 = c2 ?

a2 + b2 = 102 + 242 = 100 + 576 = 676
c2 = 262 = 676

They are equal, so ...

Yes, it does have a Right Angle!

### Example: Does an 8, 15, 16 triangle have a Right Angle?

Does 82 + 152 = 162 ?

82 + 152 = 64 + 225 = 289, but 162 = 256

So, NO, it does not have sầu a Right Angle

### Example: Does this triangle have a Right Angle? Does a2 + b2 = c2 ?

## And You Can Prove The Theorem Yourself !

Get paper pen và scissors, then using the following animation as a guide:

Draw a right angled triangle on the paper, leaving plenty of space. Draw a square along the hypotenuse (the longest side) Draw the same sized square on the other side of the hypotenuse Draw lines as shown on the animation, lượt thích this: Cut out the shapes Arrange them so that you can prove sầu that the big square has the same area as the two squares on the other sides

## Another, Amazingly Simple, Proof

Here is one of the oldest proofs that the square on the long side has the same area as the other squares.

Watch the animation, & pay attention when the triangles start sliding around.

You may want khổng lồ watch the animation a few times khổng lồ underst& what is happening.

The purple triangle is the important one. becomes We also have sầu a proof by adding up the areas.

Historical Note: while we hotline it Pythagoras" Theorem, it was also known by Indian, Greek, Chinese & Babylonian mathematicians well before he lived.
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