Question

answer the questions about the figures below.
(a) which figures are rectangles?
mark all that apply.
figure a figure b figure c none of the figures
(b) which figures are squares?
mark all that apply.
figure a figure b figure c none of the figures
(c) which figures are parallelograms?
mark all that apply.
figure a figure b figure c none of the figures

Explanation:

Step1: Recall definitions

• Rectangle: A quadrilateral with four right - angles and opposite sides equal.
• Square: A quadrilateral with four right - angles, four equal sides.
• Parallelogram: A quadrilateral with opposite sides parallel.

Step2: Analyze Figure A

Figure A has four right - angles and opposite sides equal (\(3m\) and \(2m\)). So, it is a rectangle.

Step3: Analyze Figure B

Figure B has opposite sides parallel (by the property of parallelograms: opposite sides are parallel). But it does not have four right - angles. So, it is a parallelogram.

Step4: Analyze Figure C

Figure C has four right - angles and four equal sides (\(3m\)). So, it is a square (and since a square is a special case of a rectangle and a parallelogram, it also satisfies the properties of those).

(a) Rectangles

• Figure A: Opposite sides equal and four right - angles.
• Figure C: Four right - angles (a square is a special rectangle).

(b) Squares

• Figure C: Four equal sides and four right - angles.

(c) Parallelograms

• Figure B: Opposite sides parallel.
• Figure C: Opposite sides parallel (a square is a special parallelogram).
• Figure A: Opposite sides parallel (a rectangle is a special parallelogram).

Answer:

(a) Figure A, Figure C
(b) Figure C
(c) Figure A, Figure B, Figure C