Question

for each figure, decide which category or categories describe it. choose all categories that apply
quadrilateral parallelogram trapezoid

Explanation:

Step1: Analyze the first (purple) figure

A quadrilateral is a 4 - sided polygon. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. The purple figure has 4 sides (so quadrilateral) and both pairs of opposite sides are parallel (so parallelogram). A trapezoid (in the US definition) is a quadrilateral with at least one pair of parallel sides. Since it's a parallelogram, it also satisfies the trapezoid definition (with two pairs of parallel sides). So for the purple figure: Quadrilateral (checked), Parallelogram (checked), Trapezoid (checked).

Step2: Analyze the second (blue) figure

It has 4 sides, so it's a quadrilateral. A trapezoid has at least one pair of parallel sides (the two parallel sides of the trapezoid). It is not a parallelogram because only one pair of sides is parallel (the top and bottom bases), not both pairs. So for the blue figure: Quadrilateral (checked), Trapezoid (checked), Parallelogram (not checked).

Step3: Analyze the third (red) figure

It is a square (a type of rectangle, which is a parallelogram). It has 4 sides (quadrilateral), both pairs of opposite sides are parallel (parallelogram), and since it has two pairs of parallel sides, it also satisfies the trapezoid definition. So for the red figure: Quadrilateral (checked), Parallelogram (checked), Trapezoid (checked).

Answer:

• Purple Figure: Quadrilateral (☑), Parallelogram (☑), Trapezoid (☑)
• Blue Figure: Quadrilateral (☑), Trapezoid (☑), Parallelogram (□)
• Red Figure: Quadrilateral (☑), Parallelogram (☑), Trapezoid (☑)