Pythagoras Investigation

Understanding Squares and Squareroots

The square of a number is the value you get when you multiply the number by itself.[br][math]x\times x=x^2[/math], ie the square of 7 is 49. The square root of a number is the value that when multiplied by itself gives the number. ie the square root of 9 is 3. [math]\sqrt{x^2}=x[/math],

Move point B to change the length. Click "Show Area" check box to show the square of the length, Click on the "Show Square Root" Check box to show the square root of the area.

By moving point B above and showing the area and the square root answer the following:

What is the square of 6?[br]What is the square of 4?[br]What is the square of 7.2?[br]What is the square root of 64?[br][br]Write you answers in the box below.

Pythagorus of Samos was a Greek philosopher. One of the many things he worked on was a theorem that related the lengths of the sides of a right angle triangle to each other.[br][br]You are going to investigate this relationship. Some information you will need. The two sides of the triangle that form the right angle are always the short sides. The longest side of the right angle triangle is call the Hypotenus

Move point C or point D to change the size of the triangle. The two sides that make the 90 degree angle are called the legs and also in this case the short sides of the triangle. The longest side is called the Hypontenuse

By moving point C or point D above change the size of the right angle triangle. Work out the squares of the two shorter sides and record, also record the square of the Hypotenuse which is shown to you. Do this for at least 6 different right angle triangles[br]example: for a triangle with short sides of 3 and 5 record[br]9 25 34

Can you see a relationship between the three values you recorded for each of your triangles?

Now the angle is more than 90 degrees, (You can change the angle type to less than or equal to 90 degrees with the black slider) you can now change the value of the angle,(with the green slider) and/or move points C and D to change the lengths of the leg

Change the angle and/or the lengths of the sides. record the angle and the square of each side (this time they have been given to you) Note: this time the angle must not be 90 degrees.[br][br]Does the same relationship that you found for right angle triangles still work?

For a right angle triangle where the short sides are 5 units and 12 units long, what will the square of the hypotenuse be equal to?[br][br]And therefore what is the length of the Hypotenuse?

For a right angle triangle where the short sides are 8 units and 6 [br]units long, what will the square of the hypotenuse be equal to?[br][br]And therefore what is the length of the Hypotenuse?