Geometry: inequalites

Transitive property of inequality

If a, b, and c are real numbers such that a > b and b > c then a > c.

Addition postulate of inequality

If equal quantities are added to unequal quantities, then the sums are unequal in the same order.

If unequal quantities are added to unequal quantities of the same order, the sums are unequal in the same order.

Subtraction postulate of inequalities

If equal quantities are subtracted from unequal quantities, then the differences are unequal in the same order

If unequal quantities are subtracted from equal quantities, then the differences are unequal in the opposite order.

Triangle inequality theorem

The sum of the lengths of two sides of a triangle is greater than the length of the third side of the triangle.

Length determination theorem

If two angles of a triangle are unequal, then the longer side is opposite the larger angle

triangle inequality length theorem

The sum of the lengths of two sides of a triangle is greater than the length of the third side of the triangle.