The Pythagorean Theorem applies to right triangles. The Theorem states that for all right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

\(\displaystyle a^2+b^2=c^2\)

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

\(\displaystyle a^2+b^2=c^2\)

With this equation, we can solve for a missing side length. 

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

\(\displaystyle a^2+b^2=c^2\)

In this equation:

\(\displaystyle a \textup{ and }b=\textup{legs}\)

\(\displaystyle c=\textup{hypotenuse}\)

The converse of the Pythagorean Theorem is used to determine if a triangle is a right triangle. If we are given three side lengths we can plug them into the Pythagorean Theorem formula:

\(\displaystyle a^2+b^2=c^2\)

 If the square of the hypotenuse is equal to the sum of the square of the other two sides, then the triangle is a right triangle. 

The Pythagorean Theorem can only be used to solve for the missing side length of a right triangle. Remember, the Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

\(\displaystyle a^2+b^2=c^2\)

The equation shown in the question, \(\displaystyle 5^2+12^2=13^2\), is the equation for the Pythagorean Theorem:

\(\displaystyle a^2+b^2=c^2\)

In this equation:

\(\displaystyle a \textup{ and }b=\textup{legs}\)

\(\displaystyle c=\textup{hypotenuse}\)

This means that \(\displaystyle 5\) and \(\displaystyle 12\) are the side lengths and \(\displaystyle 13\) in the hypotenuse of the triangle 

The equation shown in the question, \(\displaystyle 3^2+4^2=5^2\), is the equation for the Pythagorean Theorem:

\(\displaystyle a^2+b^2=c^2\)

In this equation:

\(\displaystyle a \textup{ and }b=\textup{legs}\)

\(\displaystyle c=\textup{hypotenuse}\)

This means that \(\displaystyle 3\) and \(\displaystyle 4\) are the side lengths and \(\displaystyle 5\) in the hypotenuse of the triangle 

The equation shown in the question, \(\displaystyle 6^2+8^2=10^2\), is the equation for the Pythagorean Theorem:

\(\displaystyle a^2+b^2=c^2\)

In this equation:

\(\displaystyle a \textup{ and }b=\textup{legs}\)

\(\displaystyle c=\textup{hypotenuse}\)

This means that \(\displaystyle 6\) and \(\displaystyle 8\) are the side lengths and \(\displaystyle 10\) in the hypotenuse of the triangle 

The equation shown in the question, \(\displaystyle 8^2+15^2=17^2\), is the equation for the Pythagorean Theorem:

\(\displaystyle a^2+b^2=c^2\)

In this equation:

\(\displaystyle a \textup{ and }b=\textup{legs}\)

\(\displaystyle c=\textup{hypotenuse}\)

This means that \(\displaystyle 8\) and \(\displaystyle 15\) are the side lengths and \(\displaystyle 17\) in the hypotenuse of the triangle 

The equation shown in the question, \(\displaystyle 2.1^2+7.2^2=7.5^2\), is the equation for the Pythagorean Theorem:

\(\displaystyle a^2+b^2=c^2\)

In this equation:

\(\displaystyle a \textup{ and }b=\textup{legs}\)

\(\displaystyle c=\textup{hypotenuse}\)

This means that \(\displaystyle 2.1\) and \(\displaystyle 7.2\) are the side lengths and \(\displaystyle 7.5\) in the hypotenuse of the triangle