Question

Based on the diagram, which reason justifies this statement? If ∠CEF is complementary to ∠DCF, then ∠DCF ≅ ∠FEG. Complements of the same angle are congruent. Complements of congruent angles are congruent. Supplements of the same angle are congruent. Supplements of congruent angles are congruen

Answer 1

Answer:

Complements of the same angle are congruent.

Step-by-step explanation:

Angles are congruent if they have the same angle measure

Angles are supplementary if their sum = 180°

Angles are complementary if their sum = 90°

∠CEF is complementary to ∠DCF

=> ∠CEF + ∠DCF = 90°

While ∠CEF & ∠FEG are also complementary

as ∠CEF + ∠FEG = 90°

Equating Both

∠CEF + ∠DCF  = ∠CEF + ∠FEG

=> ∠DCF = ∠FEG

=> ∠DCF ≅ ∠FEG

∠DCF & ∠FEG both are Complements of the ∠CEF

=> Complements of the same angle are congruent.

Answer 2

Answer:

Complements of the same angle are congruent.