1. Trigonometry
Math 10
Ms. Albarico

2. The
Pythagorean
theorem c a b

3. 5. 2 The Pythagorean Theorem A. Interpreting the Pythagorean Theorem B
5.2 The Pythagorean Theorem A. Interpreting the Pythagorean Theorem B. Pythagorean Triples

4. Students are expected to:
*Apply the Pythagorean Theorem .
*Demonstrate an understanding of and write a proof for the Pythagorean Theorem.
*Determine the accuracy and precision of a measurement.

5. Vocabulary
proof prove diagonal scissor glue paste

6. This is a right triangle:

7. We call it a right triangle because it contains a right angle.

8. The measure of a right angle is 90o

9. The little square
in the
angle tells you it is a
right angle.
90o

10. About 2,500 years ago, a Greek mathematician named Pythagoras discovered a special relationship between the sides of right triangles.

12. Pythagoras realized that if you have a right triangle,3 4 5

13. and you square the lengths of the two sides that make up the right angle,3 4 5

14. and add them together, 3 4 5

15. you get the same number you would get by squaring the other side.3 4 5

16. Is that correct? ? ?

17. It is. And it is true for any right triangle.8 6 10

18. The two sides which come together in a right angle are called

19. The two sides which come together in a right angle are called

20. The two sides which come together in a right angle are called
legs.

21. The lengths of the legs are usually called a and b.

22. The side across from the right angle is called the
hypotenuse. a b

23. And the length of the hypotenuse is usually labeled c.

24. The Pythagorean Theorem.
The special relationship between the sides of the right triangles which Pythagoras discovered is now called
The Pythagorean Theorem. c a b

25. The Pythagorean Theorem says, given the right triangle with legs a and b and hypotenuse c,

26. then c a b

27. You can use The Pythagorean Theorem to solve many kinds of problems.
Suppose you drive directly west for 48 miles, 48

28. Then turn south and drive for 36 miles.48 36

29. How far are you from where you started?48 36 ?

30. Using The Pythagorean Theorem,48
482 +
362 = c2 36 c

31. Why?
Can you see that we have a right triangle? 48 36 c
482
362 + = c2

32. Which side is the hypotenuse?
Which sides are the legs? 48 36 c
482
362 + = c2

33. Then all we need to do is calculate:

34. And you end up 60 miles from where you started.
So, since c2 is 3600, c is
60.
So, since c2 is 3600, c is 48 36 60

35. Find the length of a diagonal of the rectangle:
15"
8" ?

36. Find the length of a diagonal of the rectangle:
15"
8" ?
b = 8 c
a = 15

37. b = 8
a = 15 c

38. Find the length of a diagonal of the rectangle:
15"
8" 17

39. Practice using The Pythagorean Theorem to solve these right triangles:

40. 5 12 c
= 13

41. 10 b 26

42. = 24 10 b 26
(a)
(c)

43. 12 b 15
= 9

44. Pythagorean Triples

45. Pythagorean Triples

46. Class work! Perform Activities 3.1.1, 3.2, and 3.3.
Do as you're told right away. 100% of the work should be done in the class.
Submit the following at the end of the class:
- Activity Sheet with answers
-A4 paper with cut-outs from Activity
-A4 paper with scale drawing, answers, and completed table from Activity 3.2.
4) You may finish Activity 3.3 at home and sublit it next meeting.

47. Homework
Answer in your notebook:
Check Your Understanding
Questions # 11, 12, and 13.