**4.2: Angle Relationships in Triangles**

Definitions:

Auxiliary Lines- a line that is added to a figure to aid in a proof

Definitions:

Auxiliary Lines

**Corollary**- a theorem whose proof follows directly from another theorem

**Remote Interior Angle**- an interior angle that is not adjacent to the exterior angle

**Theorems:**

Exterior Angle Theorem- The measure of an exterior angle of a triangle is equal to the measures of its remote interior angles

Exterior Angle Theorem

**Third Angles Theorem**- If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent

**Triangle Sum Theorem**- The sum of the angle measures of a triangle is 180º

**Corollaries:**

1) The acute angles of a right triangle are complementary

2) The measure of each angle of an equiangular triangle is 60º

**Examples:**