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Pythagorean Theorem

Pythagorean Theorem. … with applications to finding area. Pythagorean Theorem. is true for all right triangles. c. a. b. Note: C must be the hypotenuse. Find x. 17. 15. x. Find x. Leave answer in SRF. x. 4. Find x. Leave answer in SRF. x. 4. Pythagorean Triples .

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Pythagorean Theorem

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  1. Pythagorean Theorem … with applications to finding area.

  2. Pythagorean Theorem is true for all right triangles. c a b Note: C must be the hypotenuse.

  3. Find x. 17 15 x

  4. Find x. Leave answer in SRF. x 4

  5. Find x. Leave answer in SRF. x 4

  6. Pythagorean Triples A Pythagorean Triple is a set of 3 whole numbers which satisfy You will be tested on these triples. (Honors only) 3, 4, 5 11, 60, 61 5, 12, 13 12, 35, 37 8, 15, 17 13, 84, 85 9, 40, 41 20, 21, 29 Note: The multiples of Pythagorean triples are also Pythagorean triples.

  7. Find the area of the parallelogram Area = (base)(height) = (10)(height) = (10)(12) = 120 sq units 10 The base is 10 because the top and bottom are congruent 13 h 5 10 Use the Pythagorean Theorem to find the height of the parallelogram Did you notice the Pythagorean Triple (5, 12, 13)? 13 h 5

  8. Find the area of the triangle. Area = ½ (base)(height) = ½ (18)(height) = ½ (18)(12) = 108 square units 15 15 h 18 Use the Pythagorean Theorem to find the height of the parallelogram 15 h Did you notice the Pythagorean Triple: (3, 4, 5) x 3 ? 9

  9. Find the area of the parallelogram. (Answer is Simplest Radical Form) Area = (base)(height) = (base)(4) = (8)(4) = 32 sq units 4 x y 4 4 x y

  10. Find the area of the triangle. (Answer in Simplest Radical Form.) Area = ½(b)(h) = ½(7)(3) = 10.5 sq units 5 h =3 3 x =4 5 h 3 3 x

  11. Homework Regular Geometry: Honors Geometry:

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