Peter and Vivian each wrote a proof for the statement: if , then is supplementary to . A supplementary angle line with angles of 1 and 2. Another obtuse angle with the angle of 3 Peter's proof: By the linear pair theorem, is supplementary to . So, . Since , then . Applying the transitive property of equality, , which means is supplementary to . Vivian's proof: Suppose is not supplementary to . So, . By the linear pair theorem, is supplementary to . By the definition of supplementary angles, . Applying the Transitive Property, . By the subtraction property of equality, this implies that . By definition of congruence, . However, contradicts the given. What type of proofs did they use? Peter used because . Vivian used because . Reset Next

Peter used direct proof method because he gets the answer directly whereas Vivian used direct proof method by contradiction because she first assumed that the answer was wrong and had to prove that the answer was right.

How to carry out Congruence Proofs?

We are told that both peter and vivian were trying to prove from the attached diagram the statement that;

If ∠2 ≅ ∠3, then ∠1 is supplementary to ∠3.

Now, from the proofs of both of them, we can see that peter used a direct proof because he knew he could get it directly but Vivian utilized another means which was by starting with contradiction to reprove that the answer was correct.

Thus, we can conclude that Peter used direct proof method because he gets the answer directly whereas Vivian used direct proof method by contradiction because she first assumed that the answer was wrong and had to prove that the answer was right.

Read more about Congruence Proofs at; https://brainly.com/question/17239468

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