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Created by G. Antidormi 2003 The Pythagorean Theorem.

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Objective The student will be able to: use the Pythagorean Theorem Designed by Skip Tyler, Varina High School

What is a right triangle? hypotenuse leg right angle leg It is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are called legs. The side opposite the right angle is the hypotenuse.

The Pythagorean Theorem In a right triangle, if a and b are the measures of the legs and c is the hypotenuse, then a2 + b2 = c2. Note: The hypotenuse, c, is always the longest side.

Find the length of the hypotenuse if 1. a = 12 and b = 16. 122 + 162 = c2 144 + 256 = c2 400 = c2 Take the square root of both sides. 20 = c

Find the length of the hypotenuse if 2. a = 5 and b = 7. 52 + 72 = c2 25 + 49 = c2 74 = c2 Take the square root of both sides. 8.60 = c

Find the length of the hypotenuse given a = 6 and b = 12 180 324 13.42 18

Find the length of the leg, to the. nearest hundredth, if 3 Find the length of the leg, to the nearest hundredth, if 3. a = 4 and c = 10. 42 + b2 = 102 16 + b2 = 100 Solve for b. 16 - 16 + b2 = 100 - 16 b2 = 84 b = 9.17

Find the length of the leg, to the nearest hundredth, if 4 Find the length of the leg, to the nearest hundredth, if 4. c = 10 and b = 7. a2 + 72 = 102 a2 + 49 = 100 Solve for a. a2 = 100 - 49 a2 = 51 a = 7.14

Find the length of the missing side given a = 4 and c = 5 1 3 6.4 9

5. The measures of three sides of a triangle are given below 5. The measures of three sides of a triangle are given below. Determine whether each triangle is a right triangle. , 3, and 8 Which side is the biggest? The square root of 73 (= 8.5)! This must be the hypotenuse (c). Plug your information into the Pythagorean Theorem. It doesn’t matter which number is a or b.

Sides: , 3, and 8 32 + 82 = ( ) 2 9 + 64 = 73 73 = 73 Since this is true, the triangle is a right triangle!! If it was not true, it would not be a right triangle.

Determine whether the triangle is a right triangle given the sides 6, 9, and Yes No Purple