Lesson 7-2: Pythagorean Theorem

1. Lesson 7-2: Pythagorean Theorem

2. Pythagorean Theorem right triangle • In a ________ ________, the sum of the squares of the ______ of a right triangle will equal the square of the ____________. • Better know as: • But I like to write: legs hypotenuse hypotenuse leg leg “Leg squared plus leg squared equals hypotenuse squared.”

3. Using Pyth. Theorem hypotenuse • When looking for the ___________: • When looking for one of the _____: Square-Add- Square Root legs “add the square of the two ________ sides, then ________ ________” Hypotenuse = square root legs Square-Subtract- Square Root hypotenuse “subtract the square of the ____________ and other _______, then ________ ________” Leg = leg square root

4. Converse of the Pyth. Thrm. backwards acute • Converse just means ____________ • This allows us to say if a triangle is __________ or _____________ obtuse Acute triangle c → _______________ a b c a Obtuse triangle → ________________ b Triple • Pythagorean __________ • A group of three whole numbers that are possible lengths in a right triangle. • 2 popular sets: ________ and ________ • ___________ of these 2 are also Pythagorean Triples. 3, 4, 5 5, 12, 13 Multiples

5. Answer: Example 2-2c Example 1 Find x.

6. Example 2-4a Example 2 Determine whether 9, 12, and 15are the sides of a right triangle. Then state whether they form a Pythagorean triple. Since the measure of the longest side is 15, 15 must be c. Let a and b be 9 and 12. Pythagorean Theorem Simplify. Add.

7. Example 3 Is a triangle with sides 3, 8, 10 acute, right, or obtuse?