Pre Algebra (Period 2 & 4)

PYTHAGOREAN THEOREM
 FOR RIGHT TRIANGLES ONLY! 11-2

2 legs - make the right angle - called a and b
(doesn't matter which is which because you will add them and adding is COMMUTATIVE!)

hypotenuse - longest side across from the right angle - called c

You can find the third side of a right triangle as long as you know the other two sides:

a² + b² = c²

After squaring the two sides that you know, you'll need to find the square root of that number to find the length of the missing side (that's why it's in this chapter!)


EASIEST - FIND THE HYPOTENUSE (c)

Example #1 from p. 510

8² + 15² = c²

64 + 225 = c²
289 = c² Take the SQ RT of each side

c = 17



A LITTLE HARDER - FIND A MISSING LEG (Either a or b)

Example #5 from p. 510

5² + b² = 13²

25 + b² = 169

b² = 169 - 25

b² = 144 Take the SQ RT of each side

b = 12



CONVERSE OF PYTHAGOREAN THEOREM

If you add the squares of the legs and that sum EQUALS the square of the longest side, it's a RIGHT TRIANGLE.


If you add the squares of the 2 smallest sides and that sum is GREATER THAN the square of the longest side, you have an ACUTE TRIANGLE.


If you add the squares of the 2 smallest sides and that sum is LESS THAN the square of the longest side, you have an OBTUSE TRIANGLE.
Check out the following website and the applet that shows why this theorem works!!
Website for the Pythagorean Theorem and its many proofs
and

Applet