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Bell Ringer

Bell Ringer. What is the measurement of the missing angles?. a. 38˚. b. c. d. a = 142°, supplementary b = 142°, alternate interior angle c = 38°, corresponding or supplementary d = 52°, triangles = 180° . Classwork /Homework. Pythagorean Theorem. Review from Friday!. Right Triangles.

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Bell Ringer

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  1. Bell Ringer What is the measurement of the missing angles? a 38˚ b c d a = 142°, supplementary b = 142°, alternate interior angle c = 38°, corresponding or supplementary d = 52°, triangles = 180°

  2. Classwork/Homework

  3. Pythagorean Theorem Review from Friday!

  4. Right Triangles Hypotenuse – Longest side is the hypotenuse, side c (opposite the 90o angle) The other two sides are the legs, sides a and b It doesn’t matter which leg is “a” or “b”. The hypotenuse is always side c! Hypotenuse (c) Leg (a) Leg (b)

  5. The Pythagorean Theorem In a RIGHT Triangle, if sides “a” and “b” are the legs and side “c” is the hypotenuse, then a2 + b2 = c2 c a b

  6. The Pythagorean Theorem Find the missing side. a2 + b2 = c2 a2 + 152 = 172 a2 + 225 = 289 a2 = 64 a = √64 = 8 17 a 15

  7. The Pythagorean Theorem Chris’ window is 12 feet high. If he placed his ladder 9 feet away from the base of the house, how long is the ladder? a2 + b2 = c2 92 + 122 = c2 81 + 144 = c2 225 = c2 √225 = c 15 feet = c Window = 12 ft Ladder = c Base = 9 ft

  8. The Pythagorean Theorem Three points are located on a coordinate plane. How long is the diagonal formed by the three points? a2 + b2 = c2 82+ 92= c2 64 + 81 = c2 145 = c2 c= √145 = 12.04 c c 8 b a 9 We could have used the distance formula to solve this!

  9. Pythagorean Triples PPF 502 - Recognize Pythagorean triples*

  10. Pythagorean Triples Pythagorean Triples are three positive whole numbers that fit the rule “a2 + b2 = c2”. The most famous triple is 3, 4, 5. This means that the legs are 3 & 4, while the hypotenuse is 5. The hypotenuse is the longest side. a2 + b2 = c2 32 + 42 = 52 9 + 16 = 25 25 = 25 This is true, so 3, 4, 5 is a triple! 5 3 4

  11. Pythagorean Triples Any multiple of a Pythagorean Triple is also true. So, any multiple of 3, 4, 5 is also a triple. 6, 8, 10 (multiply by 2) is a triple. a2 + b2 = c2 62 + 82 = 102 36 + 64 = 100 100 = 100 This is true, so 6, 8, 10 is a triple! 10 6 8

  12. Pythagorean Triples Determine whether a triangle with lengths 7, 11, and 12 form a right triangle. (The hypotenuse is always the longest length.) This is NOT true, so this is not a right triangle! a2 + b2 = c2 72 + 112 = 122 49 + 121 = 144 170 = 144 12 7 11

  13. Pythagorean Triples Determine whether a triangle with lengths 12, 16, and 20 form a right triangle. (The hypotenuse is always the longest length.) a2 + b2 = c2 122 + 162 = 202 144 + 256 = 400 400 = 400 This IS true, so this is a right triangle! 20 12 16 This is also a multiple of 3, 4, 5 triple!

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