Question

1.1 check your understanding
determine the correct type of reasoning for each of the statements within the following table.

statement	type of reasoning
traffic is always busy on friday afternoons at 4 pm. it is friday at 4 pm, so traffic will be busy.
the angles in a vertical - angle pair are congruent to each other. ∠qed and ∠saw form a pair of vertical angles, so ∠qed = ∠saw.
the measures of the two angles in a linear pair add to 180. ∠lmn and ∠pqr form a linear pair, so the measures of ∠lmn and ∠pqr add to 180.

Explanation:

1. For the statement "Nobody goes to the park when it is raining. It is raining, so nobody will be at the park", we start with a general rule (nobody goes to the park when it rains) and apply it to a specific situation (it is raining now), which is deductive reasoning.
2. For "Traffic is always busy on Friday afternoons at 4 pm. It is Friday at 4 pm, so traffic will be busy", we have a general - known pattern about traffic on Friday afternoons at 4 pm and are applying it to the current specific Friday at 4 pm, which is deductive reasoning.
3. For "The angles in a vertical - angle pair are congruent to each other. ∠QED and ∠SAW form a pair of vertical angles, so ∠QED=∠SAW", we use the general property of vertical angles and apply it to a specific pair of vertical angles, which is deductive reasoning.
4. For "The measures of the two angles in a linear pair add to 180°. ∠ABC and ∠DEF form a linear pair, so the measures of ∠ABC and ∠DEF add to 180°", we start with the general rule about linear - pair angles and apply it to a specific linear pair, which is deductive reasoning.

Answer:

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