ANSWER:
In the development of the step by step, you will find the detailed answer
STEP-BY-STEP EXPLANATION:
We have the following triangle, which is made up of two other triangles:
If the triangle ABC is right, then:
[tex]\begin{gathered} (AC)^2+(CB)^2=(AB)^2 \\ or \\ b^2+a^2=c^2 \end{gathered}[/tex]The triangle ABC and the triangle DBC by the similar triangles theorem, which says:
If the height corresponding to the hypotenuse is plotted in a right triangle, the two triangles formed are similar to each other, and similar to the given triangle.
Therefore:
[tex]\begin{gathered} \frac{c}{a}=\frac{a}{n}\rightarrow cn=a^2 \\ \frac{c}{b}=\frac{b}{m}\rightarrow cm=n^2 \end{gathered}[/tex]If we add we would be:
[tex]\begin{gathered} cn+cm=a^2+b^2 \\ c(n+m)=a^2+b^2 \\ n+m=c \\ \text{ therefore} \\ c\cdot c=a^2+b^2 \\ c^2=a^2+b^2 \end{gathered}[/tex]In this way, using the similarity between the triangles ABC and DBC, we arrive at what is the Pythagorean theorem.
