Question

which name accurately describes the figure shown below and why?

trapezoid, because it has four sides of equal length and opposite sides that are parallel
trapezoid, because it has four sides of equal length and four right angles
rhombus, because it has four sides of equal length and opposite sides that are parallel
rhombus, because it has four sides of equal length and four right angles

Explanation:

Analyze the given figure

The figure is a four-sided polygon (quadrilateral). Each of the four sides has a single tick mark, which indicates that all four sides are equal in length. The opposite sides are parallel, and the interior angles are not right angles.

Define the geometric terms

A trapezoid is a quadrilateral with at least one pair of parallel sides (or exactly one pair, depending on the definition), but it does not require four equal sides.
A rhombus is defined as a quadrilateral with four sides of equal length. By definition, its opposite sides are also parallel.

Evaluate the given options

• Option 1: "trapezoid, because it has four sides of equal length and opposite sides that are parallel" — Incorrect name.
• Option 2: "trapezoid, because it has four sides of equal length and four right angles" — Incorrect name and incorrect properties (no right angles).
• Option 3: "rhombus, because it has four sides of equal length and opposite sides that are parallel" — Correct name and accurate properties.
• Option 4: "rhombus, because it has four sides of equal length and four right angles" — Incorrect properties (it does not have right angles).

Answer:

• trapezoid, because it has four sides of equal length and opposite sides that are parallel
• trapezoid, because it has four sides of equal length and four right angles
• rhombus, because it has four sides of equal length and opposite sides that are parallel (Correct answer)
• rhombus, because it has four sides of equal length and four right angles