The Pythagorean Theorem Objective I will learn to

The Pythagorean Theorem Objective: I will learn to find the length of a side using the Pythagorean Theorem.

Interesting fact: “The name of Pythagoras was selected for this theorem not because he discovered it - the Pythagorean theorem or Pythagorean triples had been in use for centuries. -- but perhaps because Pythagoras was the first to prove theorem. ” He also did many cool inventions such as the Pythagoras Cup…

• We use the Pythagorean Theorem when we want to know the remaining length of the side of a right triangle for which we already know two lengths. • In a right triangle the 2 sides that form the right triangle are called legs. • The side opposite the right angle is called the hypotenuse. It is the longest side of the triangle. • The Pythagorean Theorem describes the relationship between the length of the hypotenuse and the length of the legs.

Watch video… https: //www. youtube. com/watch? v=Olu. Cdr. AXje 4

The Pythagorean Theorem states: In a Right Triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a 2 + b 2 = c 2

Example: Find the missing length in each right triangle. Steps to find the hypotenuse: 1. Use the Pythagorean theorem. 2. Replace a and b with their respective numbers. 3. Square a and b. 4. Add 5. Find the square root. a 2 + b 2 = c 2 32 + 4 2 = C 2 9 + 16 = C 2 25 = c 2 5 = C

Your Example:

Example 2: Find the missing length in each right triangle. Steps: 1. Use Pythagorean Theorem. 2. Replace a and b with their respective numbers. 3. Square the 2 given numbers. 4. We “undo” the addition. We do this by subtracting 36 from each side. 5. Solve. 6. Find the square root. a 2 + b 2 = c 2 a 2 + 62 = 102 a 2 + 36 = 100 - 36 a 2 = 64 a = 8

Homework: Find the missing angle in the right triangle. 1. 4. 2. 5. 3.