Warm up 1 2 3 Pythagorean Theorem n

Warm up 1. 2. 3.

Pythagorean Theorem n n n Pythagoras was a Greek philosopher and teacher He lived from 569 to 495 B. C. Often described as the “first pure mathematician”

Pythagorean theorem – only “works” for right triangles n For right triangles, where a and b are the legs and c is the hypotenuse of the triangle. Leg (b) Hy th po e te “b nu ox se ” (c )a cr os sf ro m Leg (a) n n There are more than 200 known proofs. Check out a proof of the Theorem online at http: //www. keymath. com/x 19481. xml

Ex 1: n n Identify your hypotenuse ( c ) The other two sides are legs (it doesn’t matter which on you assign a or b Plug into formula Remember order of operations - SQUARE sides first and solve 6 x a 10 b c 62 + x 2 = 102 36 + x 2 = 100 -36 x 2 = 64 x=8

Example n How high up a wall will a 20’ ladder touch if the ladder is placed 5’ from the wall? Step 1: Identify the hypotenuse and label it “c” Ladder hypotenuse 20’ Wall Label the other two sides as “a” and “b” b c Step 2: Step 3: 5’ a or Plug in and solve.

Ex 3: n Follow the steps y a -5 -5 c b

Classwork Solve for the missing side. Ex. 1 Ex. 2 5 x= 3 1 4 Ex. 3 2 6 z =5 y

Pythagorean Triples n n Any three positive integers which fit the Pythagorean equation are called Pythagorean Triples. Common Pythagorean Triples are… 3, 4, 5 5, 12, 13 7, 24, 25

Homework n Worksheet