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7.1-7.2 Pythagorean Theorem and it’s converse

7.1-7.2 Pythagorean Theorem and it’s converse. Obj : To find the missing sides of triangles To determine if measurements are for right triangles and to classify triangles. Watch video of proof of Pythagorean Thm. *Pythagorean Theorem. c. a. b.

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7.1-7.2 Pythagorean Theorem and it’s converse

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  1. 7.1-7.2 Pythagorean Theorem and it’s converse Obj: To find the missing sides of triangles To determine if measurements are for right triangles and to classify triangles

  2. Watch video of proof of Pythagorean Thm

  3. *Pythagorean Theorem c a b In a right triangle, the sum of the squares of the measures of the legs equals the square of the hypotenuse.

  4. Converse: Pythagorean Theorem Converse: If the sum of the squares of the measures of the legs equals the square of the hypotenuse then the triangle is a right triangle.

  5. Example LONGITUDE AND LATITUDE Carson City, Nevada, is located at about 120 degrees longitude and 39 degrees latitude. NASA Ames is located about 122 degrees longitude and 37 degrees latitude. Use the lines of longitude and latitude to find the degree distance to the nearest tenth degree if you were to travel directly from NASA Ames to Carson City.

  6. Solution The change in longitude between NASA Ames and Carson City is 120-122 or 2 degrees (because we can’t have a negative distance). Let this distance be a. The change in latitude is 39 - 37 or 2 degrees latitude. Let this distance be b. Use the Pythagorean Theorem to find the distance in degrees from NASA Ames to Carson City, represented by c.

  7. Pythagorean Theorem Simplify. Add. Take the square root of each side. Use a calculator. Answer: The degree distance between NASA Ames and Carson City is about 2.8 degrees.

  8. Example Find d.

  9. Answer: Pythagorean Theorem Simplify. Subtract 9 from each side. Take the square root of each side. Use a calculator.

  10. Example COORDINATE GEOMETRY Verify that is a right triangle.

  11. Solution Use the Distance Formula to determine the lengths of the sides. Subtract. Simplify. Subtract. Simplify.

  12. Solution Subtract. Simplify. By the converse of the Pythagorean Theorem, if the sum of the squares of the measures of two sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle.

  13. Example Find e and f. Answer: e = 17.9 and f = 8.9

  14. Pythagorean Triples A group of three whole numbers that satisfies the equation a2 + b2 = c2 Common triple is: 3, 4, 5 5, 12, 13 Can you find others?

  15. Classify Triangles We can use a variation of the Pythagorean theorem to help us classify triangles as well. Theorem If the square of the length of the longest side of a triangle is less than the sum of the squares of the two other sides, then the triangle is acute. Theorem If the square of the length of the longest side of a triangle is greater than the sum of the squares of the two other sides, then the triangle is obtuse.

  16. Homework • Put this in your agenda • Pg 436 1,2, 5-7, 12, 14, 25, 34, 35 • Pg 444 15-23

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