DO NOW Pythagorean Theorem Calculate the missing variable for D = RT 1). Car goes 60 mph for 6 hours   2). Plane goes 800 miles in 2 hours 3). Train goes 200 miles at 50 mph 4). Truck goes 50mph for 9 hours

What are we doing Today OBJECTIVE: WE WILL be able to calculate the sides of right triangles using the Pythagorean Theorem ESSENTIAL UNDERSTANDING: This is one of the oldest and most famous theorems in all of math. Soon you will master it! AP

Exponents and Square Roots Exponents are repeated multiplication: 42 = 4 x 4= 16 45 = 4 x 4 x 4 x 4 x 4 = 1024 A square root is the inverse of an exponent. It is the number that when multiplied by itself becomes a specified number. 52 = 25; √25 = 5 22 = 4; √4 = 2 AP

On your Calculators 1). Find the squares of the following numbers: 9 25 11 3 2). Find the square roots: √169 √25 √14 √2 AP

Historical Review Pythagorus was a Greek mathematician who founded a mathematics school in the 5th century BC in Crotone, a Greek city in Southern Italy. He (or one of his students) invented the Theorem. Legends state he was so happy he discovered it he sacrificed Oxen to the Gods. AP

What is the Pythagorean Theorem? In a right triangle (one with a 90 degree angle in it), the square of the longest side (the “hypotenuse”) is equal to the square of the two shorter sides. A2 + B2 = C2 AP

An example of the Great Theorem 1) A2 + B2 = C2 remember the long side is C, which is the unknown side here 2) 32 + 42 = C2 input values into formula 3) 9 + 16 = C2 Solve the exponents 4) 25 = C2 Combine like terms 5)√25 = √C2 Take the square root of both sides 6) 5 = C We have our answer! AP

Let’s Do These Two Together 1). 2). AP

Let’s Try Two More: AP

Follow in the steps of Pythagorus yourselves!!! AP