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The Pythgorean Theorem

The Pythgorean Theorem

Author: Sara Gorsuch
Description:

*Using the Pythagorean Theorem to find the third side of a right triangle.
*Using the Pythagorean Theorem to determine if a triangle is a right triangle.
*Defining new terms!

Showing how the pythagorean theorem works and example problems of using it!

When going through the packet, make sure to watch the khan video, at least part of it to get a better understanding, then look through my written out examples below and then go through the try on you own examples to make sure you have it all down!

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Tutorial

Pythagorean Theorem.

The Pythagorean Theorem is about dealing with the length of the sides of a right triangle. 

The equation for this is:


a2+ b2= c2

This theorem states that the sum of the squares of the lengths of the legs of a right triangle ('a' and 'b' in the triangle shown below) is equal to the square of the length of the hypotenuse ('c').

The Pythagorean theorem is used any time we have a right triangle, we know the length of two sides, and we want to find the third side or to prove that a triangle is a right triangle.


A common application of this theorem further down the line in math is the application of it in the distance formula.


Hypotenuse: Is the longest side of a triangle. 

Legs Of A Triangle: The legs are the two shorter sides of the triangle.

 


a2+b2=c2

REMEMBER:

This theorem only works on right angeled triangles!

Also,with the pythagorean theorem knowing the lengths of any two sides of a right triangle will enable you to find the length of the third side using this formula!

 

****When going through the packet, make sure to watch the khan video, at least part of it to get a better understanding, then look through my written out examples below and then go through the try on you own examples to make sure you have it all down!

Pythagorean Theorem.

Khan goes through and explains what the pythagorean theorem is, how it works and brings you through examples.

Source: Khan Academy

Example One

Example Two

Example Three

Example Four

Example Five

Practice Problems

 Formula:  a2+b2=c2

1. If a = 3 and b = 4, find the length of c.



2. If a = 4 and c = 11, find the length of b.




 

 

Answers and Steps to Practice Problems