Final answer:
The second case of the Congruent Supplements Theorem states that if two angles are congruent and each of the angles is a supplement of another angle, then the two angles that are supplements of congruent angles are congruent themselves.
Step-by-step explanation:
The second case of the Congruent Supplements Theorem states that if two angles are congruent and each of the angles is a supplement of another angle, then the two angles that are supplements of congruent angles are congruent themselves.
To prove this, let's consider two congruent angles, angle A and angle B. We know that angle A is a supplement of angle C and angle B is a supplement of angle D. Since angle A and angle B are congruent, they must have the same measure. Additionally, since angle A and angle B are supplements of angle C and angle D respectively, angle A + angle C = 180 degrees and angle B + angle D = 180 degrees. By substitution, we can say that angle C = angle D. Therefore, the two angles that are supplements of congruent angles (C and D) are congruent themselves.