1. Pythagoras Workbook

History

Pythagoras was an influential Greek mathematician and philosopher. He is best known for the theory to which he gave his name.[br]Very little is known about Pythagoras's life:[br][list][*]thought to have been born on the Greek island of Samos around 580 BC[/*][*]travelled widely in his youth, visiting Egypt and Persia[/*][*]settled in the city of Crotone in southern Italy[/*][*]thought to have been killed or died around 500 BC[/*][/list][br]While living in Crotone, Pythagoras began teaching. He attracted a number of students who lived a structured life of study and exercise, inspired by a philosophy based around mathematics. The group became known as the Pythagoreans.

Pythagoras Proof

The above is a proof of Pythagoras' theorem without words. [br][br]Pythagoras' theorem in words was as follows:[i][br][br]'The area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.' [/i][b][br][br]Please have a go at adjusting the size of the triangle and seeing if the statement holds true[/b][br][br]

Which of the below are true?

If we make two squares from the two short sides of a right angled triangle. The area of these two squares is equal to the area of a square made from the longest side of a right angled triangle. A right angled triangle has an angle of 90 degrees Pythagoras live in Crotone, Southern Italy. The above proof would work for any triangle A right angled triangle has an angle of 95 degrees The hypotenuse is the longest side of a triangle and/or the side opposite the right angle The hypotenuse is the shortest side of a triangle.

Proof with water

What do you notice from the video?

There was a right angled triangle in the video. The water from the two smaller squares filled up the larger square. The area of the two smaller squares does not equal the area of the larger square

Use the above Pythagoras tool below to help see some examples of right angled triangles. You can do this by moving the sliders.

Pythagoras Investigation

1. Choose a triangle by sliding the red and blue sliders to whatever number you would like[br]2. Take those two numbers and square them individually for example 1 squared is 1 and 2 squared is 4.[br]3. Add them those two together for example 1 + 4 = 5[br]4. Square root that using the square root button on you calculator

Use the slider app to solve the following questions.[br][br]Extension: Solve them without the slider app using the formulas below. Check your answers using the slider information.

The formula for Pythagoras is a² +b² = c²[br][br]If you know a and c then the formula to find b is b = √(c² - a²) [br][br]If you know b and c then the formula to find b is a = √(c² - b²) [br][br]If you know a and b then the formula to find b is c = √(b² + a²) [br][br]You can use all these formulas above to work out any question on Pythagoras that is below.

Read through this example of pythagoras and then practice a practical example below.

Try this below question and then swipe through to check the answer.