1. PYTHAGOREAN THEOREM Brett Solberg AHS‘11-’12

2. Warm-up  Simplify 1) 2) 3) Solve for x 5 2 = x 2 + 3 2 4) What is a hypotenuse?

3. Today’s Agenda  Test Review  Pythagorean Theorem  find missing lengths in right triangles  classify triangles  Converse  prove triangles are right triangles

4. Test Review  5 th  average 33.2/44 = 76%  high 45  6 th  average 33/44 = 75%  high 45

5. Pythagorean Theorem  Pythagoras  500 BC  Greece  Pythagoreans  Devoted to Math  Curious beliefs Fallen Objects Transmigration Sacred Beans “Knowledge is the greatest purification.”

6. Pythagorean Theorem

7.  The area of the square built upon the hypotenuse of a right triangles is equal to the sum of the areas of the squares upon the remaining sides.

8. Egypt 2600 BC

9. Babylon 1800 BC

10. China 600 BC

11. Pythagorean Theorem  In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

12. Solving

13. Examples  Find the missing side lengths

14. Examples  Find the missing side lengths

15. Pythagorean Triples  A Pythagorean Triple is a set of non-zero whole numbers a, b, c in which a 2 + b 2 = c 2 3, 4, 55, 12, 138, 15, 177, 24, 25 6, 8, 1010, 24, 2616, 30, 3414, 48, 50 9, 12, 1515, 36, 3924, 45, 5121, 72, 75 3x, 4x, 5x5x, 12x, 13x8x, 15x, 17x7x, 24x, 25x

16. Example 2  Find b in the following right triangle.  a = 7  b = ____  c = 25

17. Example 3  Is 4, 5, 6 a Pythagorean Triple?

18. Example 4  Find the distance from home base to 2 nd base.

19. Converse  The Pythagorean Theorem  If…  Then…  The Converse of the Pythagorean Theorem  If…  Then…

20. Egyptian Rope Stretchers

21. Soccer Field Example

22. Example  Is the following a right triangle?  That value of x will make the triangle a right triangle?

23. Right/Obtuse/Acute Triangles  If c 2 = a 2 + b 2 the triangle is a right triangle.  If c 2 < a 2 + b 2 the triangle is an acute triangle.  If c 2 > a 2 + b 2 the triangle is an obtuse triangle.

24. Example 5  Classify the triangles with the following side lengths  6, 11, 14  7, 8, 9

25. Homework  8.1 Worksheet and pg 420 # 2 – 16 even