PYTHAGOREAN THEOREM TRIPLES. integers A "Pythagorean Triple" is a set of positive integers, a, b and c that fits the rule: a 2 + b 2 = c 2 Example: The.

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Presentation transcript:

PYTHAGOREAN THEOREM TRIPLES

integers A "Pythagorean Triple" is a set of positive integers, a, b and c that fits the rule: a 2 + b 2 = c 2 Example: The smallest Pythagorean Triple is 3, 4 and 5. Let's check it: = 5 2 Calculating this becomes: = 25 And that is true.

The Pythagorean Triple of 3, 4 and 5 makes a Right Angled Triangle.

5, 12, 139, 40, = = = 169(try it yourself) Here are some more examples. Each has a right angle!!

Here are some more examples: (3,4,5)(5,12,13)(7,24,25)(8,15,17)(9,40,41) (11,60,61)(12,35,37)(13,84,85)(15,112,113)(16,63,65) (17,144,145)(19,180,181)(20,21,29)(20,99,101)(21,220,221) (23,264,265)(24,143,145)(25,312,313)(27,364,365)(28,45,53) (28,195,197)(29,420,421)(31,480,481)(32,255,257)(33,56,65) (33,544,545)(35,612,613)(36,77,85)(36,323,325)(37,684,685)... infinitely many more...

CONVERSE OF THE PYTHAGOREAN THEOREM Converse of the Pythagorean Theorem – If the square of the lengths of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle. If a 2 +b 2 =c 2, then the triangle is a right triangle.

APPLYING THE CONVERSE OF THE PYTHAGOREANTHEOREM

Which one of the following is NOT a Pythagorean triple? A 7, 24, 25 B 8, 15, 17 C 9, 12, 15 D 10, 16, 19

Which one of the following is NOT a Pythagorean triple? A 30, 40, 50 B 9, 40, 41 C 40, 76, 86 D 24, 32, 40

Which one of the following is a Pythagorean triple? A 5, 11, 12 B 6, 13, 14 C 7, 13, 15 D 8, 15, 17

If (x, 40, 41) is a Pythagorean triple, what is the value of x? A x = 9 B x = 10 C x = 11 D x = 12

CLASSWORK Complete the worksheet with your partner or group. 1.Complete numbers 8 – 18. Use loose leaf paper to record your answers. 2.Complete numbers 1 – 10 of the right triangle worksheet. You may record your answers on the worksheet.

HOMEWORK Complete the Pythagorean Triple worksheet and the review section at the bottom of page 102.