Question

peter and vivian each wrote a proof for the statement: if ∠2 ≅ ∠3, then ∠1 is supplementary to ∠3. peter’s proof: by the linear pair theorem, ∠1 is supplementary to ∠2. so, m∠1 + m∠2 = 180°. since ∠2 ≅ ∠3, then ∠2 = ∠3. applying the transitive property of equality, m∠1 + m∠3 = 180°, which means ∠1 is supplementary to ∠3. vivian’s proof: suppose ∠1 is not supplementary to ∠3. so, m∠1 + m∠3 ≠ 180°. by the linear pair theorem, ∠1 is supplementary to ∠2. by the definition of supplementary angles, m∠1 + m∠2 = 180°. applying the transitive property, m∠1 + m∠3 ≠ m∠1 + m∠2. by the subtraction property of equality, this implies that m∠3 ≠ m∠2. by definition of congruence, m∠3 ≠ m∠2. however, m∠3 ≅ m∠2 contradicts the given. what type of proofs did they use? peter used a direct proof because vivian used because the final statement is a contradiction evidence is used to support the conclusion

Explanation:

Answer:

Peter used a direct proof because evidence is used to support the conclusion. Vivian used an indirect proof because the final statement is a contradiction.