1. CHAPTER 8: RIGHT TRIANGLES Watch the follow clip about the Sunshine Skyway Bridge. Think about the design and construction. Do you recognize any right triangles?

2. INTEGERS Integer: One of a set of positive and negative whole numbers including zero. -3, -2, -1, 0, 1, 2, 3… When using measurements: Positive Integers N:123456789 N2N2 149162536496481 Take a look at three squares: 9, 16, and 25. Note that 9+16=25, or 3 2 + 4 2 = 5 2

3. MANIPULATING EQUATIONS 3 2 + 4 2 = 5 2 Is an equation. Can we find more numbers among the squared integers such that the sum of the two smaller squares is equal to the largest square ? Because we have an equation, we can simply multiply each side of the equation by the same number to get another equation. 3 2 + 4 2 = 5 2 (3*2) 2 +(4*2) 2 = (5*2) 2 6 2 + 8 2 = 10 2 36 + 64 = 100  TRUE

4. PYTHAGOREAN TRIPLES Integers a, b, and c form a Pythagorean Triple if a 2 + b 2 = c 2, where a and b are the smaller numbers and c is the largest. Take 5, 12, and 13. How can we tell if they are Pythagorean Triples? PLUG IT IN! Does 5 2 + 12 2 = 13 2 ? 25+144= 169 ? 169 = 169 YES, therefore they are Triples. Remember, more triples can be created by multiplying each integer in the equation by the same number.

5. PYTHAGOREAN TRIPLES Is (4, 5, 6) a Pythagorean Triple? 4 and 5 are the smaller integers; 6 is the largest 4 2 + 5 2 = 6 2 16+25=36  FALSE. (4, 5, 6) is NOT a Pythagorean Triple.

6. PRACTICE Take out personal whiteboards and determine whether each set of integers provided is a Pythagorean Theorem. Keep notes out for later.

7. PLATO’S FORMULA For any positive integer, m: (2 m ) 2 + ( m 2 – 1) 2 = ( m 2 +1) 2 Plato provided us with many awesome ideas. One of them is a way to mathematically calculate many of the Pythagorean Triples. Don’t you wish you could have hung out with him?

8. PLATO’S FORMULA (2 m ) 2 + ( m 2 – 1) 2 = ( m 2 +1) 2 Use Plato’s Formula for m=2. Check to see if your answer is a Pythagorean Triple. (2*2) 2 + (2 2 – 1) 2 = (2 2 +1) 2 (4) 2 + (3) 2 = (5) 2 16+9=25  TRUE. Plato’s Formula shows that (3,4,5) is a Pythagorean Triple.

9. PRACTICE (YOU KNOW YOU LOVE IT) Use Plato’s formula to find Pythagorean Triples for the following integers. Use a calculator if necessary. m=6 (display on whiteboard when done) Answer: (12, 35, 37) m=3 (display on whiteboard when done) Answer: (6, 8, 10)