1. In your math notebook estimate each square root: 25 36 27 111 45

2. Pythagorean Theorem

3. In a right triangle, the side opposite the right angle is the hypotenuse.

4. Pythagorean Theorem In a right triangle, the side opposite the right angle is the hypotenuse.

5. Pythagorean Theorem In a right triangle, the side opposite the right angle is the hypotenuse. Hypotenuse

6. Pythagorean Theorem In a right triangle, the side opposite the right angle is the hypotenuse. The hypotenuse is always the longest side. Hypotenuse

7. Pythagorean Theorem Legs: Hypotenuse Leg

8. Pythagorean Theorem Legs: Each of the sides forming the right angle. Hypotenuse Leg

9. Pythagorean Theorem The Pythagorean Theorem describes the relationship of the lengths of the sides of a right triangle.

10. Pythagorean Theorem The Pythagorean Theorem describes the relationship of the lengths of the sides of a right triangle. The sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

11. Pythagorean Theorem The Pythagorean Theorem describes the relationship of the lengths of the sides of a right triangle. The sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. A + B = C

12. Pythagorean Theorem The Pythagorean Theorem describes the relationship of the lengths of the sides of a right triangle. The sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. A + B = C A B C

13. Solve to find the hypotenuse:

16. Using the equation:

17. We can also use the equation to find one of the legs.

18. Using the equation: We can also use the equation to find one of the legs. To find a leg, just put in what you know and solve for the missing variable.

19. Solve to find the missing leg:

22. Pythagorean Triples: A set of three positive integers that satisfy the set: a + b = c

23. Find the distance traveled: Obama is 6.1 feet tall. The pitching mound is 60.5 feet from home plate. If Obama hits the plate, how far did the ball travel?

24. Find the distance traveled: Cruz hits a homerun clearing the wall in center field, which is 400 feet from home plate. The wall in center field is 8 feet tall. How far did the ball travel (assume he hit it off the ground)?

25. Conditional:

26. An if-then statement like, “If you live in El Paso, then you are a Texan.”

27. Conditional: An if-then statement like, “If you live in El Paso, then you are a Texan.” Hypothesis:

28. Conditional: An if-then statement like, “If you live in El Paso, then you are a Texan.” Hypothesis: The first part (after “if”).

29. Conditional: An if-then statement like, “If you live in El Paso, then you are a Texan.” Hypothesis: The first part (after “if”). Conclusion:

30. Conditional: An if-then statement like, “If you live in El Paso, then you are a Texan.” Hypothesis: The first part (after “if”). Conclusion: The second part (after “then”).

31. Conditional: An if-then statement like, “If you live in El Paso, then you are a Texan.” Hypothesis: The first part (after “if”). Conclusion: The second part (after “then”). Converse:

32. Conditional: An if-then statement like, “If you live in El Paso, then you are a Texan.” Hypothesis: The first part (after “if”). Conclusion: The second part (after “then”). Converse: Switches the hypothesis and conclusion.

33. Converse of the Pythagorean Theorem:

34. If a triangle has sides of lengths a, b, and c, and a + b = c, then the triangle is a right triangle with hypotenuse of length c.

35. Find if the triangle is a right triangle using the converse of the Pythagorean Theorem: 3 4 5

36. 5 6 7

37. Special Right Triangles:

38. 45 -45 -90 Triangles

39. Special Right Triangles: 45 -45 -90 Triangles The length of the hypotenuse = leg

40. Special Right Triangles: 30 -60 -90 Triangles

41. Special Right Triangles: 30 -60 -90 Triangles Hypotenuse = short leg 2 Longer leg = short leg

42. Find the missing sides: 45 3

43. Find the missing sides: 45 10

44. Find the missing sides: 60 30 10

45. Find the missing sides: 60 30 14

46. Assignment Page 436-438 Numbers 4-30 Even