Complementary Angles

Complementary angles are two angles that add up to 90 degrees.

T

B                            J

Theorem: If angles are complementary to the same angle, then they are congruent.  Here is how we can prove this theorem. Given:  Angle DRE is complementary             to angle ERC.            Angle TBJ is complementary            to angle ERC. Prove: Angle TBJ is congruent to angle DRE. Angle DRE is complementary to angle ERC so, angle DRE plus angle ERC is equal to 90 degrees.  Therefore angle DRE is equal to 180 minus angle ERC.  Angle ERC is complementary to angle TBJ, so angle TBJ plus angle ERC is equal to 90.  Therefore angle TBJ is equal to 180 minus angle 4.  Since angle TBJ and angle DRE have the same measure, then they are congruent. Theorem: If angles are complementary to the same angle, then they are congruent.  (The proof of this theorem is similar to the prove of the theorem above).