Question

Candice and Joel each wrote a proof for the statement: If , then . Candice's Proof Statements Reasons 1. 1. by supposition 2. 2. vertical angles theorem 3. 3. definition of congruence 4. 4. additional property of equality 5. 5. angle addition postulate Joel's Proof Statements Reasons 1. 1. given 2. 2. angle addition postulate 3. 3. vertical angles theorem 4. 4. definition of congruence 5. 5. subtraction property of equality What type of proofs did they use? Candice's proof is because . Joe's proof is because .

Answer 1

I think the answer is: Candice's proof is an indirect proof because the last statement contradicts given information. Joe's proof is a direct proof because each statement builds on logic from a previous statement.

Answer 2

Candice's proof is an indirect proof because the last statement contradicts given information. Joe's proof is a direct proof because each statement builds on logic from a previous statement.

In Mathematics and Euclidean Geometry, a proof can be defined as a series of statements (arguments) and associated reasons in sequential steps, which are used to prove that a mathematical concept, expression or idea is true.

Generally speaking, there are three main types of proof and these include the following;

1. Direct proofs
2. Indirect proof (proofs by contrapositive and contradiction).
3. Proofs by induction.

Since the last statement contradicts the given information, we can logically deduce that Candice's proof is an indirect proof. On the other hand, Joe's proof is a direct proof because each of the statements were build on logic from a preceding statement.