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PYTHAGOREAN

PYTHAGOREAN. The Pythagorean Theorem. c. The Distance Formula. a. Special Right Triangle. b. Created by ﺠﻴﻄ for mathlabsky.wordpress.com. Created by ﺠﻴﻄ for mathlabsky.wordpress.com. THE PYTHAGOREAN THEOREM.

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PYTHAGOREAN

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  1. PYTHAGOREAN The Pythagorean Theorem c The Distance Formula a Special Right Triangle b Created by ﺠﻴﻄ for mathlabsky.wordpress.com Created by ﺠﻴﻄ for mathlabsky.wordpress.com

  2. THE PYTHAGOREAN THEOREM In a right triangle, the side opposite the right angle is longest side.It is called the hypotenuse, the other side are called the legs of the triangle Theorem :the square of the length of the hypotenuse is equal to the sum of the squareof the lengths of the two legs c Hypotenuse Leg a b Leg

  3. 2. 20 cm 6 cm 16 cm 10 cm Exercise : find the length of the unknown side 1. 3. 8 cm 12 cm 4. 10 cm 5. 15 cm 5 cm 7 cm Back

  4. THE DISTANCE FORMULA To find the distance between two points A and B in the coordinate plane we can use the pythagorean theorem Y B 6 ● 6 – 3 = 3 A 3 ● 5 – 1 = 4 ● 5 ● 1 X 0

  5. Given points Aand B , find the distance between point A and B Y B A X 0

  6. Exercise : find the distance between each pair of point! • A(1, 2), B(4, -2) • P(-1, 7), Q(2, -3) • R(0, -6), S(-3, 4) • K(-3, -4), L(6, 2) • M(-2, -4), N(-6, -3) Back

  7. SPECIAL RIGHT TRIANGLE 1. Isosceles right triangel (450- 450- 900) 450 hyp x 450 x

  8. 2. Right triangle has acute angles measuring 30 and 60 (300- 600- 900) Let : ∆ABC equilateral triangle C C C 600 300 300 300 2p cm 2p cm 2p cm Long Leg Hyp 600 600 A 600 B B 600 B p cm p cm p cm D 2p cm D Short Leg D Hypotenuse = 2 x Short Leg Long Leg = Short Leg x

  9. 5. 300 x y Exercise : find the value of x and y ! 5 cm 2. 1. 600 y 3. 5 ccm 450 y x x y 6 cm 450 x 4. y 300 x 12 cm Back

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