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

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Presentation transcript:

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

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

a b c What Pythagoras Discovered: 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 = 25 Area of square on a leg + Area of square on a leg = Area of square on a hypotenuse

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

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

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

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

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

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 meters E. I need help

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 feet D. 100 feet E. I need help.