Question

2.2.6 check your understanding
determine the correct type of reasoning for each of the statements within the following table.
statement\ttype of reasoning
nobody goes to the park when it is raining. it is raining, so nobody will be at the park.
traffic is always busy on friday afternoons at 4pm. it is friday at 4pm, so traffic will be busy.
the angles in a vertical angle pair are congruent to each other. ∠qed and ∠new form a pair of vertical angles, so ∠qed≅∠new.

Explanation:

1. In the first statement, we start with a general rule ("Nobody goes to the park when it is raining") and apply it to a specific situation (it is raining now) to draw a conclusion. This is deductive reasoning.
2. The second statement also starts with a general - known pattern ("Traffic is always busy on Friday afternoons at 4 pm") and applies it to a specific instance (it is Friday at 4 pm now) to reach a conclusion, which is deductive reasoning.
3. For the third statement, we have a general geometric principle ("The angles in a vertical - angle pair are congruent to each other") and apply it to a specific pair of angles ($\angle QED$ and $\angle NEW$) to conclude they are congruent. This is deductive reasoning.

Answer:

1. Deductive Reasoning
2. Deductive Reasoning
3. Deductive Reasoning