Question

given
∠a and ∠b are supplementary
∠a ≅ ∠b
∠c is a right angle
prove
∠a ≅ ∠c
statement

1. ∠a and ∠b are supplementary
2. ∠a ≅ ∠b
3. ∠a and ∠b are right angles
4. ∠c is a right angle
5. ∠a ≅ ∠c

reason

1. given
2. given
3. supplemental right angles theorem
4. given
5. ?

what geometric reason justifies the transition from statement 4 to statement 5?
congruent right angles theorem
vertical angles theorem
substitution
congruent complements theorem

Explanation:

The Congruent Right Angles Theorem states that all right angles are congruent. Since ∠A is a right angle (from step 3) and ∠C is a right angle (given in step 4), by this theorem, ∠A ≅ ∠C.

Answer:

Congruent Right Angles Theorem