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 is expressed as: $$c^2 = a^2 + b^2$$ .

The Pythagorean Theorem ONLY works on right triangles.

In a right triangle, side c (the hypotenuse) is ALWAYS the longest side.

Yes, the triangle with sides 5, 12, and 13 is a right triangle because it satisfies the Pythagorean Theorem: $$5^2 + 12^2 = 13^2$$ .

The formula to find the length of the hypotenuse (c) is: $$c = \text{sqrt}(a^2 + b^2)$$ .

To find a missing side (x) in a right triangle, you can use the formula: $$x^2 = c^2 - a^2$$ or $$x^2 = c^2 - b^2$$ depending on which side is missing.

Using the Pythagorean Theorem: $$21^2 - 15^2 = x^2$$ , we find that the length of the other side is $$\text{sqrt}(21^2 - 15^2) = \text{sqrt}(441 - 225) = \text{sqrt}(216)$$ .

In a right triangle, the relationship between the sides is defined by the Pythagorean Theorem: the sum of the squares of the two shorter sides equals the square of the longest side.

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

Using the Pythagorean Theorem: $$c = \text{sqrt}(8^2 + 6^2) = \text{sqrt}(64 + 36) = \text{sqrt}(100) = 10$$ .