Lesson 7-2: Pythagorean Theorem

Pythagorean Theorem In a ________ ________, the sum of the squares of the ______ of a right triangle will equal the square of the ____________. Better know as: Also think of it as: “Leg squared plus leg squared equals hypotenuse squared.” leg hypotenuse legs triangleright hypotenuse

Find the missing sides:

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

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

Converse of the Pyth. Thrm. Converse just means ____________ If a triangle is not right, the pythagorean theorem can tell us if it is is __________ or _____________ → _______________ → ________________ backwards acute obtuse Acute triangle Obtuse triangle a b c b a c

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. Triple 3, 4, 55, 12, 13 Multiples

Example 2-4a Determine whether 9, 12, and 15 are 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. Example 2

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