Question

1. select all statements that could be the first step of an indirect proof of the conditional below. if m∠2 = 95, then m∠3 = 95. a. if m∠3 ≠ 95, then m∠2 ≠ 95. b. if m∠2 = 95, then m∠3 = 95. c. assume if m∠3 ≠ 95, then m∠2 ≠ 95. d. assume if m∠2 ≠ 95, then m∠3 ≠ 95. e. assume if m∠3 = 95, then m∠2 = 95.

Explanation:

Step1: Recall indirect proof concept

In an indirect proof of a conditional statement "If \(p\), then \(q\)" (\(p
ightarrow q\)), the first - step is to assume the negation of the conclusion and the truth of the hypothesis. The given conditional is "If \(m\angle2 = 95\), then \(m\angle3 = 95\)" where \(p:m\angle2 = 95\) and \(q:m\angle3 = 95\). The first step of an indirect proof should start with assuming the opposite of the conclusion while keeping the hypothesis in mind.

Step2: Analyze each option

• Option A is the contra - positive of the original statement, not the first step of an indirect proof.
• Option B is the original statement, not the first step of an indirect proof.
• Option C: Assuming "if \(m\angle3

eq95\) (negation of the conclusion), then \(m\angle2
eq95\)" is a correct first step for an indirect proof as it starts by considering the situation where the conclusion is false.

• Option D is not the correct first step as it negates the hypothesis first.
• Option E is not correct as it does not start by negating the conclusion.

Answer:

C. Assume if \(m\angle3
eq95\), then \(m\angle2
eq95\)