Mathematical Theorems and Laws

The Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees. This theorem is a fundamental property of triangles and is used in many areas of mathematics and geometry.

The Pythagorean Theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. This theorem is one of the most well-known and important theorems in mathematics and has been used for centuries in many different fields.

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. This theorem is a fundamental property of triangles and is used in many areas of mathematics and geometry.

The Law of Cosines states that the cosine of the angle between two sides of a triangle is equal to the ratio of the product of the lengths of the two sides to the product of the lengths of the other two sides. This law is a generalization of the Pythagorean Theorem and is used in many areas of mathematics and geometry.

The Area of a Triangle Theorem states that the area of a triangle is equal to half the product of the base and the height. This theorem is a fundamental property of triangles and is used in many areas of mathematics and geometry.

The Volume of a Rectangular Prism Theorem states that the volume of a rectangular prism is equal to the product of its length, width, and height. This theorem is a fundamental property of rectangular prisms and is used in many areas of mathematics and geometry.

The Surface Area of a Rectangular Prism Theorem states that the surface area of a rectangular prism is equal to the sum of the areas of its six faces. This theorem is a fundamental property of rectangular prisms and is used in many areas of mathematics and geometry.

The Volume of a Sphere Theorem states that the volume of a sphere is equal to four-thirds pi times the radius cubed. This theorem is a fundamental property of spheres and is used in many areas of mathematics and geometry.

The Surface Area of a Sphere Theorem states that the surface area of a sphere is equal to four pi times the radius squared. This theorem is a fundamental property of spheres and is used in many areas of mathematics and geometry.

The Angle Sum Theorem for Polygons states that the sum of the interior angles of a polygon with n sides is equal to (n-2) * 180 degrees. This theorem is a fundamental property of polygons and is used in many areas of mathematics and geometry.

The Area of a Circle Theorem states that the area of a circle is equal to pi times the radius squared. This theorem is a fundamental property of circles and is used in many areas of mathematics and geometry.

The Circumference of a Circle Theorem states that the circumference of a circle is equal to two pi times the radius. This theorem is a fundamental property of circles and is used in many areas of mathematics and geometry.

The Volume of a Cylinder Theorem states that the volume of a cylinder is equal to pi times the radius squared times the height. This theorem is a fundamental property of cylinders and is used in many areas of mathematics and geometry.

The Surface Area of a Cylinder Theorem states that the surface area of a cylinder is equal to two pi times the radius times the height plus two pi times the radius squared. This theorem is a fundamental property of cylinders and is used in many areas of mathematics and geometry.

The Volume of a Cone Theorem states that the volume of a cone is equal to one-third pi times the radius squared times the height. This theorem is a fundamental property of cones and is used in many areas of mathematics and geometry.