Pythagorean Theorem Practice

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: $$c^2 = a^2 + b^2$$ .

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

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

Using the Pythagorean Theorem: $$c^2 = 3^2 + 4^2 = 9 + 16 = 25$$ , so $$c = 5$$ .

The distance formula is: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ .

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1 : $$\sqrt{3}$$ : 2.

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is $$\sqrt{2}$$ times the length of a leg.

The area of a right triangle can be found using the formula: $$Area = \frac{1}{2} \times base \times height$$ .

The converse states that if in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Pythagoras was an ancient Greek mathematician who is best known for formulating the Pythagorean Theorem.