Pythagorean Theorem

The side opposite the right angle is called the opposite side.

The side adjacent to the right angle is called the adjacent side.

The opposite side in a right triangle is always shorter than the hypotenuse.

The Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the squares of the adjacent and opposite sides.

The Pythagorean Theorem is often written as $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the adjacent and opposite sides, respectively, and $c$ is the length of the hypotenuse.

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $6^2 + b^2 = 10^2$. Solving for $b$, we get $b = 8$ cm.

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $a^2 + 5^2 = 13^2$. Solving for $a$, we get $a = 12$ cm.

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $8^2 + 6^2 = c^2$. Solving for $c$, we get $c = 10$ cm.

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $a^2 + 12^2 = 20^2$. Solving for $a$, we get $a = 16$ cm.

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $8^2 + b^2 = 17^2$. Solving for $b$, we get $b = 15$ cm.

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $10^2 + b^2 = 26^2$. Solving for $b$, we get $b = 24$ cm.

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $a^2 + 7^2 = 13^2$. Solving for $a$, we get $a = 12$ cm.

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $a^2 + 20^2 = 25^2$. Solving for $a$, we get $a = 15$ cm.

Using the Pythagorean Theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $a^2 + 9^2 = 15^2$. Solving for $a$, we get $a = 12$ cm.