1. Pythagorean Theorem Eman Almasruhi 3/1/2015

2. Objectives : Students will know the right triangle. Recognize Pythagorean Theorem. Do some example to show how the formula works. Students will be able to solve the problem.

3. A right angle is an internal angle, which is equal to 90°. A right angle can be in any orientation or rotation as long as the internal angle is 90°. 90900 90° Right Angle

4. The hypotenuse is the largest side in a right triangle and is always opposite the right angle. (Only right triangles have a hypotenuse). The other two sides of the triangle, AC and CB are referred to as the 'legs' A Right Triangle's Hypotenuse leg Hypotenuse Right angle (a (b (c

5. Practice Find the right triangle Circle all the right triangles below

6. The Pythagorean theorem, also known as Pythagoras's theorem, is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Pythagorean theorem a b c

7. The Pythagorean theorem: The sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. This formula is a 2+ b 2= c 2 Pythagorean theorem Formula a 2+ b 2= c 2 a b c

8. If we know the lengths of two sides of a right angled triangle, we can find the length of the third side. Example A "3,4,5" triangle has a right angle in it. a 2 + b 2 = c 2 3 2 + 4 2 = 5 2 9 + 16 = 25 3 2 + 4 2 gives you 25 and 5 2 gives you 25. in this case 3 2 + 4 2 gives you the same number as 5 2 there for your answer for c is correct. C=5 the length of the hypotenuse is 5. 1 1 25 16 9 5 4 3

9. Order of operations dictates that the values should be squared before they are added. 3 x 3 = 9 and 7 x 7 = 49. The sum of 9 and 49 is 58, or 9 + 49 = 58. To cancel the square of c, the right side of the equation, we must take the square root of both sides. The square root of a square of a value is equal to the original value. If we must take the square root of the right side, the same must be done to the left side. The square root of 58 is 7.6157. Only four decimal places of an infinitely long, non-repeating answer has been displayed. Example B Solve for C a=3 B=7 (c

10. 5 12 c Real World Example In this example we want to know the hypotenuse of lift side of the roof. A 2 + b 2 = c 2 5 2 + 12 2 = c 2 25 + 144 = c 2 c 2 = 169 c = √169 c = 13

11. Practice Problems Solve for a, b, or c a? c? a=5 b=4 b=3 c=2 b? a=7 c=6