Question

Peter and Vivian each wrote a proof for the statement: if 22 23, then 21 is supplementary to 23.
1
Peter used
because
2
Peter's proof:
By the linear pair theorem, 21 is supplementary to 22. So, m/1 + m/2 = 180°. Since 2223, then 22 = 23. Applying the transitive property
of equality, m/1 + m/3 = 180°, which means 21 is supplementary to 23.
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3
Vivian's proof:
Suppose 21 is not supplementary to 23. So, m/1 + m23 180°. By the linear pair theorem, 21 is supplementary to 22. By the definition of
supplementary angles, m/1 + m/2 = 180°. Applying the Transitive Property, m/1 + m23 # m/1 + m2. 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?
e because
B. Vivian used

Answer 1

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

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