Question

how can this quadrilateral be classified?
select each correct answer.
trapezoid
parallelogram
rhombus
square

Explanation:

Step 1: Analyze the quadrilateral's properties

The quadrilateral \( EFGH \) has all sides marked as equal (the tick marks) and a right angle at \( H \). Let's recall the definitions:

• Trapezoid: A quadrilateral with at least one pair of parallel sides. In a square (which this appears to be), there are two pairs of parallel sides, so it is a trapezoid (in some definitions, a trapezoid has exactly one pair, but in inclusive definitions, at least one; since a square has two, it qualifies).
• Parallelogram: A quadrilateral with both pairs of opposite sides parallel. A square has opposite sides parallel, so it is a parallelogram.
• Rhombus: A quadrilateral with all sides equal in length. The tick marks show all sides are equal, so it is a rhombus.
• Square: A quadrilateral with all sides equal, all angles right angles, and opposite sides parallel. This figure has equal sides, a right angle, and parallel sides (implied by equal sides and right angle), so it is a square.

Step 2: Confirm each classification

• Trapezoid: Since it has parallel sides (opposite sides are parallel), it is a trapezoid (using the inclusive definition where a trapezoid has at least one pair of parallel sides).
• Parallelogram: Opposite sides are equal and parallel (from the square properties), so it is a parallelogram.
• Rhombus: All sides are equal (tick marks), so it is a rhombus.
• Square: All sides equal, right angle, and parallel sides, so it is a square.

Answer:

trapezoid, parallelogram, rhombus, square