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TEOREMA DE PITAGORAS

Pythagoras THEOREM

To speak of another proof of the theorem of Pythagoras mention Euclidean movements.


* Rotation: to make a rotation is needed at the point around which will make the rotation and an angle that determines how many degrees is this.

parallel
* Translations:
To make a parallel translation takes a segment AB. If a point Q moves to a point Q 'on AB, then the length of QQ' is equal to the length of AB and QQ 'is parallel to AB, while QA is parallel to Q `B.


* Reflection and symmetry
To make a reflection or symmetry is making a line called the axis of reflection or symmetry axis.
Thus if a point is in the axis of symmetry, the reflection is the same point, ie that the line is reflected in itself. Any other point on the plane is reflected across the axis of symmetry.



Another proof of the theorem of Pythagoras

Three Euclidean transformations can be used to give another demonstration of the Pythagorean theorem, namely: the whole triangle, the sum of the squares of the lengths of the legs equals the square the length of the hypotenuse.

Be A `BC a right triangle where BC is the hypotenuse.
Now make the following changes:


1. By reflection symmetry axis BC, obtain the right triangle ABC.


2. For translation, according to BC, the triangle ABC we subtract the triangle T1.

3. By rotating 90 ° around, we subtract the triangle T2.

4. With the triangle T2 is repeated step 2 and continues until the triangle T6.

is clear that the hypotenuse of the triangle ABC, T2, T4 and T6 are all equal to BC and that two consecutive 90-degree angle form. This means that they form a square.

As the area of \u200b\u200bthe square is (BC) 2 and square area can be found in the area of \u200b\u200b5 parts that compose it, namely the four equal triangles and square then you must: