The Congruent Complements Theorem states that if two angles are complements of the same angle (or of congruent angles), then those two angles are congruent to each other.
To explain this further, let’s break it down:
- Complementary angles are two angles whose measures add up to 90 degrees.
- If angle A and angle B are complementary to angle C, then according to the theorem, angle A is congruent to angle B.
For instance, if angle C is 30 degrees, then angle A can be 60 degrees (together they make 90 degrees), and angle B can also be 60 degrees (because it is also complementary to angle C). Because both angle A and angle B are 60 degrees, the theorem holds true that angle A is congruent to angle B.
This theorem is useful in geometric proofs and can help simplify problems involving angles.