Question

peter and vivian each wrote a proof for the statement: if ∠2 ≅ ∠3, then ∠1 is supplementary to ∠3. peters 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. vivians proof: suppose ∠1 is not supplementary to ∠3. so, m∠1 + m∠2 = 180°. applying the transitive property of equality and the definition of congruence, m∠3 ≅ m∠2. what type of proofs did they use? peter used because. vivian used because.

Explanation:

Peter started with known facts (linear - pair theorem) and used logical steps to directly reach the conclusion. Vivian started by assuming the opposite of what needed to be proven and then showed that this led to a contradiction.

Answer:

Peter used a direct proof because he used evidence (linear - pair theorem, transitive property of equality) to support the conclusion. Vivian used an indirect proof because the final statement is a contradiction (assuming the opposite of the conclusion led to a false situation).