Educator

Pythagorean Theorem

• A right triangle is a triangle which has a right angle. The side opposite the right angle, called the hypotenuse, is the longest side of the triangle. The two sides forming the right angle are called the legs of the triangle.

• The Pythagorean Theorem states that if a right triangle has legs of lengths a and b, and hypotenuse of length c, then a² + b² = c².

• This result can be used to find the length of any side of a right triangle if the other two sides are known.

• Some triples (a, b, c) of whole numbers, such as (3, 4, 5), satisfy the Pythagorean Theorem. Such triples are called Pythagorean triples. Note that any multiple of a Pythagorean triple is also a Pythagorean triple.

• The converse of the Pythagorean Theorem, which is also true, states that if the sides a, b, and c of a triangle satisfy the equation a² + b² = c², then the triangle is a right triangle.