If two angles are complementary, that means that their sum is
90∘.
Two angles form a pair of complementary, supplementary and vertical angles. When the sum of two angles is
90∘, they are called complementary angles. Such a relationship may be useful in determining other unknown angles.
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Complementary Angle Theorem
Statement: If two angles are each complementary to a 3rd angle, then they are congruent to each other. Or complements of the same angle are congruent.
Proof: Let
∠A and
∠B be complementary angles.
Step 1:
∠B is a complement of
∠A Then
∠A+∠B=90∘ (By complementary angles definition)
Step 2: Let
∠A and
∠C be complementary angles.
⇒∠C is a complement of
∠A Then,
∠A+∠C=90∘ From Step 1 and Step 2 we have,
∠A+∠B=∠A+∠C ⇒∠B=∠C