Pythagoras Theorem

Developed by a Greek mathematician, Pythagoras of Samos, Pythagoras theorem is not just some triangles and their sides drawn on a piece of paper. It is a universal principal that can be seen in everything we see and do. For example, taking a shortcut in a road,

construction,


 and even in our shadow.



Pythagoras theorem shows the relationship between 3 sides of a right angled triangle. To understand this, lets first look at how be label the sides. 

The side opposite to the right angle in a triangle or what you might recognize more as the longest side of a right angled triangle is called the hypotenuse.

 


After identifying the hypotenuse, the other 2 sides can be labelled a and b. The order doesn't matter.

Now for the sake of writing down an equation, were going to represent hypotenuse as c. The exact relation between these 3 is that square of 'a' plus square of 'b' will be equal to square of 'c'. Hence, we derive the following equation from this information:

To see this more clearly, look at the picture below


Now the real focus here is using this formula to find an unknown side. If we know any 2 of these sides we can find the third side thanks to this relation. For example, look at the question below,

We know the 'a' and 'b' sides of this triangle so for the first step of finding the hypotenuse or the 'c' side, we just follow the formula and add 5 squared with 7 squared. But remember, by doing this we'll get the square of hypotenuse so the answer we get here isn't quite the final answer yet. To find the final answer, we have to take the square root of this answer, like so:

Now this seems quite easy right? But unfortunately, we can't end this lesson here. This question is so simple because it is asked to find the hypotenuse here but sometimes we will be asked to find one of the other 2 sides and this makes the process a little different. 

for example lets look at another question,


Here the hypotenuse is given so when we substitute the value we know into the formula, it will look this this, 
Now you see how this is different right? but do not fear, we can solve this simple problem just by applying a simple algebraic rule and rearranging the formula. We need b squared as the subject of this formula so we remove the 4 squared at the front and bring it to the left hand side. But when we do this, the sign chances to the inverse of the original so the positive 4 squared changes to negative 4 squared.
From here on, we proceed the same way as in the last question. 
The only difference between the 2 is that in the second type of questions, we have to rearrange the formula before solving. Hence, it is very important to read it thoroughly and identify which type of question it is before starting.

Here is a little diagram to help you with that, 

Now I am well aware that some of you will find reading all that above troublesome and hard to understand but not to worry, I have included a short video on this right below. just click the link. Hope you find it helpful 

Pythagoras theorem.mp4 

I think we all have a very clear understanding of the Pythagoras theorem and how to do questions on it but we can't be completely sure without trying for ourselves can we? I have included a worksheet and a short quiz on this below. Make sure you go through them and before you leave.

Worksheet:
Pythagoras theorem.pdf 

Quiz: 
https://kahoot.it/challenge/0825627?challenge-id=fce05bca-e50a-4334-bddd-75cf60734864_1713948921957 

Or go to Kahoot and use the code 0825627 

Good Luck!













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