The Pythagorean Theorem Pythagoras a + b = c 2 2 2

Pythagorean Theorem Leg Leg Hypotenuse 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 Hypotenuse Leg Leg

25 C 2 2 5 2 A 2 3 9 2 4 2 B 16

2 5 2 4 2 3 C 2 A 2 B 2 9 16 25

a c b Pythagorean Theorem Leg Leg Hypotenuse Identify the sides of this right triangle a Hypotenuse c Leg b Leg

a b c Pythagorean Theorem Leg Leg Hypotenuse Identify the sides of this right triangle Leg a b c Leg Hypotenuse

a b c Pythagorean Theorem 1 3 2 Identify the sides of this right triangle 3 a b c 1 2

c a b Pythagorean Theorem 1 3 2 Identify the sides of this right triangle 1 c 2 a b 3

Pythagorean Theorem a + b = c 5 + 7 = c 25 + 49 = c 74 = c 8.6 = c Find the length of the missing side. a + b = c 2 2 2 x 5 + 7 = c 2 2 2 25 + 49 = c 2 5 cm 74 = c 2 8.6 = c 7 cm

Pythagorean Theorem a + b = c 6 + 8 = c 36 + 64 = c 100 = c 10 = c Find the length of the missing side. a + b = c 2 2 2 x 6 + 8 = c 2 2 2 36 + 64 = c 2 6 cm 100 = c 2 10 = c 8 cm

Pythagorean Theorem a + b = c 3 + 5 = c 9 + 25 = c 34 = c 5.8 = c Find the length of the missing side. a + b = c 2 2 2 x 3 + 5 = c 2 2 2 9 + 25 = c 2 3 cm 34 = c 2 5.8 = c 5 cm

Pythagorean Theorem a + b = c 20 + 21 = c 400 + 441 = c 841 = c 29 = c Find the length of the missing side. a + b = c 2 2 2 20 + 21 = c 2 2 2 20 in 400 + 441 = c 2 841 = c 2 29 = c 21 in

a + b = c a + b = c a + 12 = 13 a + 144 = 169 a = 5 -144 -144 a = 25 2 12 cm a + 144 = 169 2 -144 -144 13 cm a = 25 2 a = 5

17 in 15 in Answer = 8 in

24 in 25 in Answer = 7 in

11 10 9 8 7 x 6 6 x 8 5 Answer = 7.8 4 Answer = 8.9 3 5 2 4 1 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 -1 -2 -3 7 Yellow = 7.8 Blue = 8.9 Green = 9.2 Purple = 7.3 -4 -5 -6 Answer = 9.2 6 -7 x 7 x Answer = 7.3 -8 -9 -10 2 -11

11 10 9 8 7 6 5 19 4 3 x 2 1 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 -1 -2 -3 X = 26.9 -4 -5 -6 -7 -8 -9 19 -10 -11

Pythagorean Theorem x Find the height of the building. 70 ft (Round to the nearest ft) 70 ft x Answer = 49 ft 50ft

Do not measure the desk directly. Use the Pythagorean theorem to measure the height of the desk in centimeters. Do not measure the desk directly. Tape the end of the fishing line to the floor 2 meter fishing line Measure this distance in cm

Converse of the Pythagorean Theorem If the square of the length of one side of a triangle is equal to the sum of the squares of the length of the other two sides, then the triangle is a right triangle. a + b = c 2 2 2 3 + 4 = 5 2 2 2 9 + 16 = 25 25 = 25

Identify a Right Triangle The measure of three sides of a triangle are 5 inches, 12 inches, and 13 inches. Determine whether the triangle is a right triangle. a + b = c 2 2 2 2 2 5 + 12 = 13 2 25 + 144 = 169 169 = 169

Identify a Right Triangle The measure of three sides of a triangle are 8 inches, 10 inches, and 15 inches. Determine whether the triangle is a right triangle. a + b = c 2 2 2 2 2 8 + 10 = 15 2 64 + 100 = 225 164 = 225

Identifying an Obtuse Triangle If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, the triangle is obtuse a + b c 2 2 < 2 2 + 3 4 2 2 < 2 4 + 9 16 < 13 16 <

Identifying an Acute Triangle If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, the triangle is acute. a + b c > 2 2 2 > 2 6 + 7 8 2 2 > 36 + 49 64 85 64 >

Pythagorean triple Is a set of nonzero whole numbers a, b, and c that satisfy the equation a + b = c 2 2 2 Here are some common Pythagorean triples 7,24,25 3,4,5 5,12,13 8,15,17