Example of Argument of the Pythagorean Theorem

The argumentation is the part of a speech or exposition in which we expose in a logical way, consistent and coherent the point of view that we want to demonstrate, the elements that we are exposing and the conclusion. It also serves to expose and explain a topic in a logical and coherent way, so that there is no doubt.
In the formal logic, the argumentation, is the exposition in which we state a thesis or idea to be demonstrated, and the premises by means of which we try to demonstrate our thesis. Unlike the demonstration, where we present the facts (premises) to lead to our thesis, in the argumentation we will also establish the connections between each of the premises, and why the relationships between the premises lead us to conclude that the thesis we hold is true. To achieve this, a semantic convention must be established; This means agreeing on the meaning that words will have, especially those that may represent a contextual or meaning difficulty, to know exactly what is being talked about and the scope of each word.

The argumentation is used in the fields of teaching, scientific research, philosophy, religion, law and politics, and allows us to achieve a clear and firm exposition of what we want to demonstrate.
Argumentation Example:
The Pythagorean theorem.
The Pythagorean theorem was stated many centuries ago, it tells us that the sum of the square of the legs is equal to the square of the hypotenuse, referring to a right triangle.
To understand it, we are going to define:
Right triangle: It is a triangle in which one of the angles measures 90 °, that is, it has a right angle.
Hypotenuse: It is the side opposite the right angle, and the longest side of the triangle.
Leg: It is each one of the minor sides of the triangle; both legs coincide at right angles.
To understand the Pythagorean theorem, we will use measurements in whole numbers, which allow us to do the calculations with less difficulty.
We will start by drawing a horizontal line with a length of 4 centimeters. Now, at one end of the line, we will draw a 3 centimeter line at right angles. Now we have a right angle, with two sides, 3 and 4 centimeters; these are the legs. We only need to join the ends of each line, to form the triangle. If we measure the length of this last line, we will realize that it measures exactly 5 centimeters.
Since we have drawn our right triangle, we proceed to take the accounts:
32=9
42=16
16+9=25
52=25
Therefore, when adding the square of the measure of the legs, the result is equal to the square of the measure of the hypotenuse. No matter the size of the legs, and the hypotenuse, the relationship will always be the same.