Algebra Period 3 (Wednesday)

PYTHAGOREAN THEOREM 11-7
(an old friend) -
FOR RIGHT TRIANGLES ONLY!
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
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
b = 12

ONE THAT YOU WOULDN'T HAVE HAD IN PRE-ALGEBRA:
One of the legs = √5
√5² + b² = 13²
5 + b² = 169
b² = 169 - 5
b² = 164
√ b2 = √164
b = √4•41
b = 2√41

DISTANCE FORMULA
(based on the Pythagorean Theorem):
see p. 513 in book
The distance between any two points on the coordinate plane (x y plane)
The distance is the hypotenuse of a right triangle that you can draw using any two points on the coordinate plane (I'll show you how to draw it in class).

The formula is:
distance = √[( difference of the two x's)² + (difference of the two y's)²]
distance = √(x₁-x₂)² + (y₁- y₂)²
The difference between the 2x’s is the length of the leg parallel to the y axis and
the difference between the 2y’s is the length of the leg parallel to the x axis
The difference of the two x's is length of one of the two legs
The difference of the two y's is the length of the other leg
The distance is the length of the hypotenuse
So you could actually rewrite the distance formula to look like the Pythagorean Theorem:
c = √[a² + b²]

EXAMPLE: What is the distance between (3, -10) and (-7, -2)?
d = √[(3 - -7)² + (-10 - -2)²]
d = √[10² +( -8²)]
d = √(164)
Simplifying:
2√41
Check out the following website- with its 81 different proofs
Pythagorean Theorem and its many proofs. See if you can find the proof that is attributed to one of our US Presidents
Practice your skills with the Pythagorean Theorem using this Shodor Interactive Site at
Pythagorean Explorer