Pythagorean Theorem

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: $$a^2 + b^2 = c^2$$ .

To find the length of the hypotenuse (c) in a right triangle, use the formula: $$c = \text{sqrt}(a^2 + b^2)$$ .

The hypotenuse is the longest side of a right triangle, opposite the right angle.

The Pythagorean Theorem only applies to right triangles.

Using the Pythagorean Theorem: $$c = \text{sqrt}(3^2 + 4^2) = \text{sqrt}(9 + 16) = \text{sqrt}(25) = 5 cm$$ .

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

Use the formula: $$b = \text{sqrt}(c^2 - a^2)$$ . Here, $$b = \text{sqrt}(10^2 - 6^2) = \text{sqrt}(100 - 36) = \text{sqrt}(64) = 8 cm$$ .

A right triangle is a triangle that has one angle measuring 90 degrees.

The legs of a right triangle are the two sides that form the right angle.

No, the Pythagorean Theorem cannot be used for obtuse triangles; it only applies to right triangles.