Geometry 5

The “ Three Possibilities” Property

Either a is greater than, equal to, or less than b

The Transitive Property

If a is greater than b and b is greater than c, then a is greater than c

The Addition Property

If a is greater than b, the a + c is greater than b + c

The Subtraction Property

If a is grater than b, then a - c is greater than b - c

The Multiplication Property

If a is greater than b and c is greater than 0, then ac is greater than bc.

The Division Property

If a is greater than b and c is greater than 0, then a/c is greater than b/c

The Addition Theorem of Inequality

If a is greater than b and c is greater than d, then a + c is greater than b + d

The “ Whole Greater than Part” Theorem

If a is greater than 0, b is greater than 0, and a + b = c, then c is greater than a and b

Definition of exterior angle of a triangle

An exterior angle of a triangle is an angle that forms a linear pair with an angle of the triangle

The Exterior Angle Theorem

An exterior angle of a triangle is greater than either remote interior angle.

Theorem 13 (unequal)

If two sides of a triangle are unequal, the angles opposite them are unequal in the same order

Theorem 14

If two angles are unequal, the sides opposite them are unequal in the same order

Theorem 15- The Triangle Inequality Theorem

The sum of any two sides of a triangle is greater than the third side