what is pythagorean theroem

Question

Hi, i am in the 8th grade and they are teaching us about Pythagorean Theroem but I have no clue what it is.

Answer 1

Meena's answer is correct, but usually in math books the 90^o angle is at "C" and so the hypotenuse is "c".  The formula becomes a² + b² = c².  

To answer your question about what it is, in common terms, it is a way to find the length of one leg of a right triangle when you know the other 2 leg lengths. So if you know a and b then you you can find c. If you are given a and c then you can find b. If you are given b and c then you can find a.

Answer 2

Hi Alona,

 

Pythagorean Theorem:

 

In a right  triangle, The sum of the  squares of the lengths of the legs is equal to the  square of the length of the hypotenuse.

 

For triangle ABC, ∠B = 90°

 

 

b= length of Hypotenuse of triangle, a & c are lengths of legs.

 

so  b²= a² + c²

                                                                                                    

 

 

 

 

Answer 3

Hello, Alona

The Pythagorean Theorem sounds scary because of its weird name, which half the people cannot pronounce or spell.  But it is very simple.  

 

The Pythagorean Theorem only applies to right triangles.  So, if it is not a right triangle, you cannot use it.

 

In a right triangle, the two smaller sides are called the LEGS. 

 

The longest side is called the HYPOTENUSE.  This side is always opposite the right angle.

 

Problems dealing with the Pythagorean Theorem fall in two categories.

1) Problems where you need to find the longest side, hypotenuse.

2) Problems where you need to find one of the legs.

 

If you are looking for the hypotenuse, these are the steps:

 

a) square both legs.  Lets say that the legs are 5 and 12.  You are going to square both numbers.  And you square numbers by multiplying the numbers by themselves.  So, 5^2 becomes 25 and 12^2 becomes 144.

 

b) add the squared legs. In this case, add 25+ 144 = 169. DO NOT ADD THE LEGS BEFORE YOU SQUARE THEM. This a mistake that a lot of my students make, so don't do it.

 

c) Find the square root of the sum of the squared legs.  The square root of 169 is 13.  So, the hypotenuse is 13.  Note, that 13, the hypotenuse, is greater than the legs. This is a quick way to check whether you did the problem right.

 

If you are looking for a leg, these are the steps. (To keep it simple, I am going to use 5 and 13.  Our answer should be 12... Shhhh. Pretend you don't know)

 

a) Square theHypotenue.  The hypotenuse is 13 since the hypotenuse must always be the longest side.  So, 13^2= 169

b) Square the given leg.  In this case, it will be 5^2= 25

c) subtract (hypotenuse)^2 - (leg)^2.  169-25 = 144

d) Take the square root the answer from step c, which is 12

 

This is what I tell my students: 

a) for hypotenuse: square,square, add, radical

b) for the leg: square, square,subtract, radical

 

 I hope this helps. 

 

D.Y. Taylor

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