Learn Pythagoras' Theorem Squares and Sides
Learn to use the relationship
Teacher version
Interactive lesson part 1
Interactive lesson part 2
Explain how to calculate the area of the largest square.
Pythagoras' Theorem says that if we construct squares on the three sides of a right triangle, the two smaller squares will fit perfectly into the largest square. The largest square lies opposite the right angle.
On the next applet, move the green and yellow pieces so that they fit perfectly into the largest square.
Change the triangle around to make sure it works on all kinds of right-triangles.
For every adding fact, there are two subtracting facts.
Use 'subtract' to calculate the area of the third square when the area of the largest square and one of the smaller squares is given.
On the next applet, you need to decide whether to add or subtract.
Explain how you know whether to add the two given areas or to subtract.
On the next applet, all the squares are blue.
The triangle rotates around.
Be sure to identify the longest side before deciding whether to add or subtract.
The longest side lies opposite the right angle.
The name of the longest side on a right-angled triangle is the 'hypotenuse'.
The big deal about the Pythagorean theorem is that the squares help us to calculate the sides of the right triangle.
Use the square root button on your calculator to find the length of each side of the triangle in the next applet.
In the next applet, two sides are given. Complete all the answer boxes.
To find the area of the third square, you will need to either add or to subtract the areas of the other two squares.
In this final applet the squares are hidden and the triangle rotates on each new question. You can imagine the squares on each side, or you can click on the 'show squares' button.
Calculate the areas of the squares, then calculate the length of the missing side.