The Pythagorean Theorem leg hypotenuse leg Applies to Right Triangles only! The side opposite the right angle The sides creating the right angle are called.

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Presentation transcript:

The Pythagorean Theorem leg hypotenuse leg Applies to Right Triangles only! The side opposite the right angle The sides creating the right angle are called the “legs.” The largest side is called the “hypotenuse.”

The Pythagorean Theorem leg hypotenuse leg “The sum of the squares of the lengths of the legs is equal to the square of the hypotenuse.”

The Pythagorean Theorem a c b “The sum of the squares of the lengths of the legs is equal to the square of the hypotenuse.”

The Pythagorean Theorem a c b “The sum of the squares of the lengths of the legs is equal to the square of the hypotenuse.” a 2 + b 2 = c 2 “The sum of the squares of the lengths of the legs is equal to the square of the hypotenuse.” a 2 + b 2 = c 2 “The sum of the squares of the lengths of the legs is equal to the square of the hypotenuse.” a2 + b2 = c2a2 + b2 = c2 a2 + b2 = c2a2 + b2 = c2

The Pythagorean Theorem a c b “The sum of the squares of the lengths of the legs is equal to the square of the hypotenuse.” a 2 + b 2 = c 2 Special Cases:Isosceles Right Triangles a c a a 2 + a 2 = c 2 2a 2 = c

The Pythagorean Theorem a c b “The sum of the squares of the lengths of the legs is equal to the square of the hypotenuse.” a 2 + b 2 = c 2 Special Cases:Isosceles Right Triangles 8 c = c 2 Example: a = 8 a a = c = c 2 2a 2 = c

The Pythagorean Theorem a c b “The sum of the squares of the lengths of the legs is equal to the square of the hypotenuse.” a 2 + b 2 = c 2 Special Cases:Isosceles Right Triangles 4 c 2a 2 = 4 2 Example: c = 4 a a 2a 2 = 16 a 2 = 8 2a 2 = c

The Pythagorean Theorem a c b “The sum of the squares of the lengths of the legs is equal to the square of the hypotenuse.” a 2 + b 2 = c 2 Special Cases:Equilateral Triangles a c b b c += c 2b = c 2b2b2b2b a 2 + b 2 = c 2 a 2 + b 2 = (2b) 2 a 2 + b 2 = 4b 2 a 2 = 3b

The Pythagorean Theorem a c b “The sum of the squares of the lengths of the legs is equal to the square of the hypotenuse.” a 2 + b 2 = c 2 Special Cases:Equilateral Triangles a c b b c + 2b = c 2b2b a 2 = Example: b = a 2 = 3b = c14 = c

The Pythagorean Theorem a c b “The sum of the squares of the lengths of the legs is equal to the square of the hypotenuse.” a 2 + b 2 = c 2 Special Cases:Equilateral Triangles a c b b c + 2b = c 2b2b a 2 = Example: c = a 2 = 3b 2 2b = 6 b = 3

The Pythagorean Theorem a c b “The sum of the squares of the lengths of the legs is equal to the square of the hypotenuse.” a 2 + b 2 = c 2 Special Cases:Equilateral Triangles a c b b c + 2b = c 2b2b 18 2 = 3b 2 Example: a = a 2 = 3b = 3b = b = b 2