Question

How to visualise Pythagorean theorem?

Answer 1

Visualize the Pythagorean theorem.

Pythagorean theorem: Pythagorean theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base, and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle ${90}^{\circ }$. The sides of a right triangle (say $a$, $b$ and $c$) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.

Consider the triangle given above:

Where $a$ is the perpendicular, $b$ is the base and $c$ is the hypotenuse.

According to the definition, the Pythagoras theorem formula is given as:

$$\begin{gathered} Hypotenus{e}^2=Perpendicula{r}^2+Bas{e}^2 \\ \Rightarrow c^2=a^2+b^2 \end{gathered}$$

Consider three squares of sides $a$, $b$, $c$ mounted on the three sides of a triangle having the same sides as shown.

By Pythagoras theorem

Area of square $a+$ Area of square $b=$ Area of square $c$

Hence, the Pythagorean theorem is stated as, “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.