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Based on this diagram, the following conditional statement holds true. The sum of angles 1 and 2 is 90^(∘). The sum of angles ∠ 2 and ∠ 3 is also 90^(∘). Since both angles ∠ 1 and ∠ 3 are each complementary to angle ∠2, they are congruent.
m∠ 1 + m∠ 2 = 90^(∘) m∠ 2 + m∠ 3 = 90^(∘) ⇒ ∠ 1 ≅ ∠ 3
The Congruent Complements Theorem also applies when two angles are complementary to congruent angles.
Based on this pair of diagrams, the following conditional statement holds true. The sum of angles ∠1 and ∠2 is 90^(∘). The sum of angles ∠3 and ∠4 are also complentary, so their sum is also 90^(∘). If angle ∠1 is congruent to angle ∠4, then by the Congruent Complements Theorem, it follows that angle ∠2 is congruent to angle ∠3.
m∠ 1 + m∠ 2 = 90^(∘) m∠ 3 + m∠ 4 = 90^(∘) ∠ 2 ≅ ∠ 3 ⇒ ∠ 1 ≅ ∠ 4
The sum of measures of complementary angles is equal to 90^(∘). In this case, ∠ 1 and ∠ 2, and ∠ 2 and ∠ 3 are pairs of complementary angles. m∠ 1 + m∠ 2 = 90^(∘) m∠ 2 + m∠ 3 = 90^(∘) Therefore, m∠ 1 + m∠ 2 and m∠ 2 + m∠ 3 are equal by the Transitive Property of Equality. m ∠ 1 + m∠ 2 = m∠ 2 + m∠ 3 Using the Subtraction Property of Equality, this equation can be simplified by subtracting m∠ 2 from both sides. m ∠ 1 + m∠ 2 = m∠ 2 + m∠ 3 ⇓ m∠ 1 = m∠ 3 Two angles have equal measures when they are congruent.
∠ 1 ≅ ∠ 3