1. Pythagorean Theorum Ahmed Fallatah

2. At the end of this presentation you will be able to identify a right triangle, use the Pythagorean Theorem to calculate the lengths of the hypotenuse of a right triangle and calculate any missing leg of a right triangle Objectives

3. None About Pythagoras

4. The general concept of Pythagorean Theorem indicates that In a right angled triangle the square of the hypotenuse Which is C here the longest side of the triangle is equal to the sum of the squares of the other two sides A and B. a b c Right Triangle What is Pythagorean Theorem

5. This model will show you how the Pythagorean Theorem equation works. This is the previous picture but we transfer it to the equation. If you sum the size of a and b squires it will be equal to the size of c squire. a2a2 b2b2 c2c2 +=

6. To know how much this theory involved in our daily life solving problems imagine you are locked out of your house and the only open window is on the second floor, 25 feet above the ground. you need to borrow a ladder from one of your neighbors. There's a bush along the edge of the house, so you'll have to place the ladder 10 feet from the house. What length of ladder do you need to reach the window? Real World Example

7. Which one of these triangles is a right triangle. To recognize a right triangle look for any angle equal to 90°, does not matter the rotation or the orientation of the triangle. 6. Right triangle and hypotenuse

8. Let us work on this equation and see how to solve this problem. Note; second picture will appear after we work on the first triangle. 3 45 Example 1 a b c

9. This is another example but remember that A right angle can be in any orientation or rotation 5 12 C Example 2

10. Now is your turn to practice the theory. But will ask in a different formula: Does this triangle have a Right Angle? Practice 1 10 24 26

11. I think you already have noticed that we have the value of the hypotenuse and we need to calculate the value of b. Identifying any missing leg 9 b 15 9 12 15

12. Now is your turn to practice the equation. Find out the value of b. 4 b 5 4 3 5 Practice 1

13. Now is your turn to practice the equation. Find out the value of b. 4 b 5 4 3 5 Practice 1