# Can someone explain pythagoras better than my teacher?

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all she said was a2 + b2=c2

all she said was a2 + b2=c2

##### 3 Answers

Pythagoras' Theorem helps to find missing sides in any right angle triangle so long as you know the other two sides.

#### Explanation:

Pythagoras' Theorem helps to find missing sides in any right angle triangle so long as you know the other two sides. For example;

In this triangle we can see that we are missing the side 'b'.

In the equation:

We need to subsitute the numbers from the triangle into the equation so we work out:

We need to rearrange this equation to figure out, side b.

We then solve this equation to find

I'll use the **similar triangle method** to prove here, there are a lot more :)

Consider

Consider

Addind these two,

Note that

Therefore, the Pythagoras statement, can be written as,

Read below.

#### Explanation:

We have a right triangle here:

We also can draw the following:

That looks like a square... but let's prove it.

First, we can see that the side lengths of the green quadrilateral are all equal.

Now, we label like the following:

Using the fact that the angles of a triangle add up to 180 degrees, we see that the missing angle of the triangle, (the one opposite to side

We now have:

Using the fact that a straight line has an angle of 180 degrees, the missing angle of the green quadrilateral is:

You can use the same technique for the other three angles and see that the green quadrilateral is indeed a square.

Therefore, the area of the green square is:

Let's draw another sketch:

You can use the same technique that I used for the previous square to prove that the green quadrilaterals there are squares.

We see that the area of the green squares is:

The large square that contains both the squares and triangles for both cases have the same side length (

Since we have four congruent triangles for each sketch, the leftover areas (the green squares) must be equal to each other.

Therefore:

Which tells that the length of the longest side of a right triangle squared is equal to the sum of the other sides squared.

An example would be

Note that there are hundreds of ways to prove the theorem.