Question

Why does the Pythagorean theorem only work for right triangles?

Answer 1

Pythagoras theorem: In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the there two sides.

Let's consider a $△ABC$, where $AB=2cm,BC=3cmandAC=4cm$

We know that hypotenuse is the longest side of a triangle.

For $△ABC$, side $AC$ is a hypotenuse.

Using Pythagoras theorem, we get

${\left(AC\right)}^2={\left(AB\right)}^2+{\left(BC\right)}^2$

$\Rightarrow$ ${\left(4\right)}^2={\left(2\right)}^2+{\left(3\right)}^2$

$\Rightarrow$ $16=4+9$

$\Rightarrow$ $16=13$

This is not possible.

Thus, the Pythagoras theorem does not work for this triangle.

Since the hypotenuse is the longest side of the triangle and is opposite the right angle.

Hence we can say that the Pythagorean theorem only works for right triangles.