Supplementary Angles

Supplementary angles are angles that add up to 180 degrees.

Theorem: If angles are supplementary to the same angle, then they are congruent.  Here is how we can prove this theorem. Given:  Angle 3 is supplementary to             angle 4.            Angle B is supplementary to            angle 4. Prove:  Angle 3 is congruent to angle B. Angle 3 is supplementary to angle 4, so angle 3 plus angle 4 is equal to 180, therefore angle 3 is equal to 180 minus angle 4.  Angle B is supplementary to angle 4, so angle B plus angle 4 is equal to 180, therefore angle B is equal to 180 minus angle 4.  Since angle 3 and angle B have the same measure, we can conclude that they are congruent. Theorem: If angle are supplementary to congruent angles, then they are congruent.  (The proof of this theorem is similar to the theorem above).