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Objective The student will be able to:

This lesson, designed by Skip Tyler from Varina High School, focuses on the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): (a^2 + b^2 = c^2). Students will explore how to find the lengths of the hypotenuse and legs of right triangles using provided examples and practice problems. By the end of the lesson, students will grasp the concept of right triangles and become proficient in applying the theorem.

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Objective The student will be able to:

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  1. ObjectiveThe student will be able to: use the Pythagorean Theorem Designed by Skip Tyler, Varina High School

  2. 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

  3. 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.

  4. 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

  5. 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

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

  7. 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

  8. 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

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

  10. 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.

  11. 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.

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

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