1. The Pythagorean Theorem We are learning to…solve for the missing side of right triangles using the Pythagorean Theorem. Sunday, January 24, 2016

2. The Pythagorean Theorem Right Triangle – a triangle with one right angle Make a drawing of a right triangle. Why can a right triangle not have more than one right angle? Hypotenuse – the longest side of a right triangle; can always be found across from the right angle on a right triangle. Label the hypotenuse on your drawing. Leg of a Right Triangle – the two other sides of the triangle which are not the hypotenuse Label the legs on your drawing. Hypotenuse Leg

3. a b c What Pythagoras Discovered: 3 4 5 3 5 4 The area of squares built on the legs of a right triangle are equal to the sum of the area of the square built on the hypotenuse. 25 square units 9 square units 16 square units (a)(a) + (b)(b) = (c)(c) a 2 + b 2 = c 2 …this is known as the Pythagorean Theorem We can use the Pythagorean Theorem to solve for missing sides of right triangles. 9 + 16 = 25 Area of square on a leg + Area of square on a leg = Area of square on a hypotenuse

4. The Pythagorean Theorem Example #1 5 cm 12 cm ? We are looking for the hypotenuse! a 2 + b 2 = c 2 5 2 + 12 2 = c 2 25 + 144 = c 2 169 = c 2 The missing length of the hypotenuse is 13 centimeters long.

5. The Pythagorean Theorem Example #2 25 ft 24 ft ? We are looking for a leg! a 2 + b 2 = c 2 a 2 + 24 2 = 25 2 a 2 + 576 = 625 a 2 + 576 – 576 = 625 – 576 a 2 = 49 a = 7 The missing length of the leg is 7 feet.

6. The Pythagorean Theorem Example #3 8 m 15 m ? We are looking for the hypotenuse! a 2 + b 2 = c 2 8 2 + 15 2 = c 2 64 + 225 = c 2 289 = c 2 The missing length of the hypotenuse is 17 meters long.

7. The Pythagorean Theorem Example #4 20 in 29 in ? We are looking for a leg! a 2 + b 2 = c 2 a 2 + 20 2 = 29 2 a 2 + 400 = 841 a 2 + 400 – 400 = 841 – 400 a 2 = 441 a = 21 The missing length of the leg is 21 inches.

8. Find the length of the missing side of the right triangle below: 48 m ? 20 m A. 43 meters B. 50 meters C. 52 meters D. 68 meters E. I need help. 1234567891011121314151617181920 21222324252627282930

9. A rectangular garden has the dimensions shown below. 29 m 20 m Find the missing length of the garden. ? A. 441 meters B. 25 meters C. 21 meters D. 35.2 meters E. I need help. 1234567891011121314151617181920 21222324252627282930

10. In class, Juanita sits directly in front of Harold, 8 feet away, and directly to the left of Ian, 6 feet away. What is the distance, in feet, from Ian to Harold? A. 10 feet B. 14 feet C. 5.29 feet D. 100 feet E. I need help.