4.2: Angle Relationships in Triangles
Definitions:
Auxiliary Lines - a line that is added to a figure to aid in a proof
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
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:
Definitions:
Auxiliary Lines - a line that is added to a figure to aid in a proof
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
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: