In a right-angled triangle on the plane, the square of the length of two right-angled sides adds up to the square of the length of the hypotenuse.

(as shown in the figure below, that is, a? + b？ = c？ )

Example:

Take the right triangle in the above picture as an example. If the side length of A is 3 and the side length of B is 4, we can calculate the side length of C by Pythagorean theorem.

From the pythagorean theorem, a? + b？ = c？ → 3? +4 = c

That is 9+16 = 25 = C.

c =？ √25 = 5

So we can use Pythagorean theorem to calculate that the side length of C is 5.

Extended content:

Pythagorean theorem:

Pythagorean theorem, also known as quotient height theorem, Pythagorean theorem, Pythagorean theorem and Bainiu theorem, is a basic and important theorem in plane geometry. Pythagorean theorem shows that the sum of squares of the lengths of two right-angled sides of a right-angled triangle on a plane (called hook length and head in ancient times) is equal to the square of the length of hypotenuse (called chord length in ancient times). On the other hand, if the sum of squares of two sides of a triangle on the plane is equal to the square of the third side, it is a right triangle (the opposite side of the right angle is the third side). Pythagorean theorem is one of the important mathematical theorems discovered and proved by human beings in the early days.

Inverse theorem of Pythagorean theorem;

The inverse theorem of Pythagorean theorem is a simple method to judge whether a triangle is obtuse, acute or right, where AB=c is the longest side:

If a? + b？ = c, then △ABC is a right triangle.

If a? + b？ & gtC, then △ABC is an acute triangle (if there is no condition that AB=c is the longest side, then the formula only satisfies that ∠C is an acute angle).

If a? + b？ & ltc, then △ABC is an obtuse triangle.

References:

Pythagorean Theorem-Wikipedia