Question

given
∠a and ∠b are complementary
∠c ≅ ∠b
∠d and ∠c are complementary
prove
∠a ≅ ∠d.
what geometric reason justifies the transition from
statement 1 and 4 to statement 5?

1. ∠a and ∠b are complementary
2. given
3. ∠c ≅ ∠b
4. given
5. ∠d and ∠c are complementary
6. given
7. ∠d and ∠b are complementary
8. substitution
9. ∠a ≅ ∠d
10. ?

congruent right angles theorem
supplementary right angles theorem
vertical angles theorem
congruent complements theorem

Explanation:

Step1: Recall the Congruent Complements Theorem

The Congruent Complements Theorem states that if two angles are complementary to the same angle (or to congruent angles), then the two angles are congruent.
In this case, from statement 1 (\(\angle A\) and \(\angle B\) are complementary) and statement 4 (\(\angle D\) and \(\angle B\) are complementary), \(\angle A\) and \(\angle D\) are both complementary to \(\angle B\).

Answer:

Congruent Complements Theorem