The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The properties of a parallelogram include opposite sides being parallel and equal in length, opposite angles being equal, and consecutive angles being supplementary.

A triangle can be proven to be a right triangle by using one of the following methods: (1) showing that one angle measures 90 degrees, (2) showing that the Pythagorean theorem is true for the triangle, or (3) using the fact that the hypotenuse and one of the legs of a right triangle are similar to the legs of the triangle.

The formula for the area of a circle is A = πr^2, where A is the area, π is approximately equal to 3.14, and r is the radius of the circle.

A regular polygon is a polygon where all sides are equal in length and all angles are equal in measure. An irregular polygon is a polygon that does not have all sides or angles equal in measure.

A protractor is used to measure angles. It is a tool that has a scale, usually in degrees, and a base that can be placed against the vertex of an angle, allowing the user to read the measure of the angle.