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use the Pythagorean Theorem Lesson Oct. 6-10, 2009 Dr. N. Parker

M8G2: a. Apply properties of right triangles, including the Pythagorean theorem. b. Recognize and interpret the Pythagorean theorem as a statement about areas of squares on the sides of a right triangle. use the Pythagorean Theorem Lesson Oct. 6-10, 2009 Dr. N. Parker. Redan Middle School.

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use the Pythagorean Theorem Lesson Oct. 6-10, 2009 Dr. N. Parker

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  1. M8G2:a. Apply properties of right triangles, including the Pythagorean theorem. b. Recognize and interpret the Pythagorean theorem as a statement about areas of squares on the sides of a right triangle. use the Pythagorean Theorem Lesson Oct. 6-10, 2009 Dr. N. Parker Redan Middle School

  2. Vocabulary • right triangle, properties, Pythagorean Theorem, slope, radicands • Expressions, square root, perfect squares, radical, positive number,

  3. What is a right triangle? hypotenuse leg right angle 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. leg

  4. 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.

  5. Find the length of the hypotenuse if1. a = 12 and b = 16. 122 + 162 = c2 144 + 256 = c2 400 = c2 Take the square root of both sides. 20 = c

  6. Find the length of the hypotenuse if2. a = 5 and b = 7. 52 + 72 = c2 25 + 49 = c2 74 = c2 Take the square root of both sides. 8.60 = c

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

  8. Find the length of the leg, to the nearest hundredth, if3. a = 4 and c = 10. 42 + b2 = 102 16 + b2 = 100 Solve for b. 16 - 16 + b2 = 100 - 16 b2 = 84 b = 9.17

  9. Find the length of the leg, to the nearest hundredth, if4. c = 10 and b = 7. a2 + 72 = 102 a2 + 49 = 100 Solve for a. a2 = 100 - 49 a2 = 51 a = 7.14

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

  11. 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.

  12. Sides: , 3, and 832 + 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.

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

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