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Pythagoras Theorem Cutouts

In the previous posts, two different explorations were presented for the derivation of the Pythagoras Theorem. The first exploration can be found here and the second here.

The Pythagoras Theorem states that:
   "The square of the length of the hypotenuse (denoted by c) is equal to the sum of the squares of the lengths of the other two sides (denoted by a and b)"

Pythagoras Theorem

This post is for the downloadable cutouts for each of the explorations. You may download them and use them for your class or for your kids to learn.

Here is the cutout for the first exploration of the Pythagoras Theorem. The file consist of two pages. The first page consists of four congruent right triangles. The second page is a square.

Cut along the broken lines on the right triangles and use them to fill in the square on the second page using the EXPLORATION 1 as a guide.

You comments and suggestions are welcome here. You may write them in the comment box below.

The Pythagorean Theorem

Here is another proof for the Pythagorean Theorem. You can see the first part here.

The Pythagoras' Theorem

The Pythagorean theorem is also known as the Pythagoras' theorem. It is named after a famous Greek mathematician, Pythagoras, who is credited for its proof.

The theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the remaining sides. That is c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the lengths of the remaining sides.

Here is one of the theorem. Take note that the theorem only applies to right triangles.
Start with a cutout of any right triangle.
 Let us name the shortest side as a, the longer side as b and the hypotenuse as c.
Let us make three (3) more of the right triangle.
Our next step is to form a square out of the four (4) triangles, making sure that the combined length of a and b will be the length of the side of the square that we are forming.


Let us take a look at the different parts of the square we formed. If we separate the whole square, we can get its area in terms of a and b.

The middle part is also a square with sides equal to the hypotenuse of the right triangle. The area can also be obtained.

The area of the four right triangles outlining the sides of the whole square is as follows

We take note that the area of the whole square is equal to the area of the small square in the middle added to the area of the four right triangles. That is
Thus, c^2 = a^2 + b^2.

Hope this will help you understand the derivation of the Pythagoras' Theorem.

Your comments and suggestions are welcome here. You may write them in the comment box below. Thank you!

Here is the two-column proof for the EXTERIOR ANGLE THEOREM. You may download and print it for your perusal.

Many are already familiar with the angles of a triangle. Many can easily point out which are the interior angles and even draw the exterior angles.