Question

2.2.6 check your understanding
which of the following represent deductive reasoning? select all that apply.
the measures of the two angles in a linear pair add to 180°. ∠ntr and ∠mkg form a linear pair, so the measures of ∠ntr and ∠mkg add to 180°.
birds fly south for the winter. a penguin is a bird so it will fly south in the winter.
the sum of the measures of the interior angles of any triangle is 180°. polygon qag is a triangle, so the sum of the measures of its interior angles must be 180°.
traffic is always busy on friday afternoons at 4pm. it is friday at 4pm, so traffic will be busy.
all rectangles are quadrilaterals. a square is a rectangle, so a square must be a quadrilateral.

Explanation:

Deductive reasoning starts with general principles and applies them to specific cases.

1. General principle: Linear - pair angles sum to 180°. Specific case: ∠NTR and ∠MKG are a linear pair, so they sum to 180°. This is deductive reasoning.
2. The statement about penguins is incorrect as penguins don't fly south for winter despite being birds. But the form of reasoning (general rule about birds flying south applied to a specific bird) is deductive.
3. General principle: Sum of interior angles of a triangle is 180°. Specific case: Polygon QAG is a triangle, so its interior - angle sum is 180°. This is deductive reasoning.
4. General principle: Traffic is busy on Friday afternoons at 4 pm. Specific case: It's Friday at 4 pm, so traffic will be busy. This is deductive reasoning.
5. General principle: All rectangles are quadrilaterals. Specific case: A square is a rectangle, so a square is a quadrilateral. This is deductive reasoning.

Answer:

All of the above statements represent deductive reasoning. So the selected options are all the check - boxes.