77.1k views
0 votes
Provide the proof for the second case of the Congruent Supplements Theorem.

User Qingsong
by
7.7k points

1 Answer

7 votes

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.

User ObiWanKenobi
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.