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