**The Pythagorean Theorem states that**
**the sum of the squares**
**of the two small sides of a right triangle is equal
to**
**the square of the third side.**

**This can be summarized by the equation**
**a^2 + b^2 = c^2**
**(The caret ("^") is used here to indicate raised
to a power.**
**a^2 = "a squared" = a x a)**

**The two short sides of a right triangle are**
**the sides that are connected to the right angle,**
**often indicated by a small box inside the corner.**

**When you know the lengths of the two short sides (a
and b),**
**you can square each of them and add them together.**
**Then take the square root, and you have the length
of**
**the third side (c)**

**For example, say that you know that the two short sides
of a triangle**
**are 5 and 12. Then let a = 5 and b = 12.**

**You must find the length of the**
**hypotenuse (the long side) which we will call c.**

**a^2 + b^2 = c^2**
**5^2 + 12^2 = c^2**
**25 + 144 = c^2**
**169 = c^2**
**so c = the square root of 169, which is 13 (13 x 13
= 169).**

**For example, suppose you know that one of the short
sides is 8 and the long**
**side is 10. Then let a = 8 and c = 10.
Solve for b.**

**8^2 + b^2 = 10^2**
**64 + b^2 = 100**

**Subtract 64 from each side to get:**
**b^2 = 36**
**so b = 6.**

**Most problems that use the Pythagorean Theorem**
**utilize multiplies of what are known as Pythagorean
Triples.**

**The first two are (3, 4, 5)
and (5,12, 13).**

**While there are many more,**
**if you are aware of these triples and are**
**on the lookout for multiples of them**

**such as (6, 8, 10 or
10, 24, 26),**

**you can often find missing sides**
**without actually using the Pythagorean Theorem.**

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