1. PYTHAGOREAN THEOREAM http://www.youtube.com/watch?v=uaj0XcLtN5cwww.youtube.com/watch?v=uaj0XcLtN5c http://www.youtube.com/watch?feature=player_detailpage&v=DRRVu- RHQWEwww.youtube.com/watch?feature=player_detailpage&v=DRRVu- RHQWE

2. What is the relationship among the lengths of the sides of a right triangle http://www.youtube.com/watch?v=uaj0XcLtN5c

3. Calculating this becomes: 9 + 16 = 25 WIKIPEDIA CCSC Alignnment: 8.G.B.6

4. Pythagoras applied to similar triangles

5. Pythagoras by pentagons

6. Trig Functions

7. One of the best known mathematical formulas is Pythagorean Theorem, which provides us with the relationship between the sides in a right triangle. A right triangle consists of two legs and a hypotenuse. The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle.

8. Write it down as an equation: abc triangle a^2 + b^2 = c^2

9. The Pythagorean Theorem tells us the relationship in every right triangle a^2+b^2=c^2

10. Example:

11. Example: Does this triangle have a Right Angle? 10 24 26 triangleDoes a^2 + b^2 = c^2 ?C^2 = 10^2+24^2 = 676They are equal, so...Yes, it does have a Right Angle!

12. Let's check if the areas are the same: 3^2 + 4^2 = 5^2Calculating this becomes:9 + 16 = 25

13. It works... like Magic! Example: Solve this triangle. A^2 + b^2 = c^2 5^2 + 12^2 = c^2 25 + 144 = c2 169 = c2 C^2 = 169 c = √169 c = 13

14. example: Does this triangle have a Right Angle? Triangle with roots 3 + 5 = 8 ? Yes, it does! So this is a right-angled triangle (√3)^2 + (√5)^2 = (√8)^2 ?

15. Leg^2 + leg^2 = hypotenuse ^2

16. You Can Prove The Theorem Yourself !

17. proof of the Pythagorean Theorem and it converse: In any right triangle, the sum of the squares of the legs equals the square of the hypotenuse (leg2 + leg2 = hypotenuse2). The figure below shows the parts of a right triangle. Leg^2 + leg^2 = hypotenuse^2 hypotenuse2 – leg2 = leg2

18. proof 3^2 + 4^2 = x^2 26^2 – 24^2 =x^2 9 + 16 = x^2 676 – 576=x^2 √25 = √x^2 √100 = √x^2 10 = x √25 = x 5 = x

19. distance formula: The distance d between the points A = (x1, y1) and B = (x2, y2) is given by the formula: The distance formula can be obtained by creating a triangle and using the Pythagorean Theorem to find the length of the hypotenuse. The hypotenuse of the triangle will be the distance between the two points. √

20. distance formula

21. For example, consider the two points A (1,4) and B (4,0), so: x1 = 1, y1 = 4, x2 = 4, and y2 = 0. Substituting into the distance formula we have:

22. Sides relationships

23. PRACTICAL APPLICATION

24. SOH, CAH, TOA

25. The Pythagorean theorem

26. Right Angle Trignometry