Question

choose all answers that describe the polygon ghij if gh = 19, hi = 19, ij = 19, jg = 19, gh ⊥ hi, hi ⊥ ij, ij ⊥ jg, and jg ⊥ gh. answer choices: parallelogram, quadrilateral, rectangle, rhombus, square, trapezoid

Explanation:

1. Quadrilateral: A polygon with four sides. GHIJ has four sides (GH, HI, IJ, JG), so it is a quadrilateral.
2. Rectangle: A quadrilateral with four right angles (since \(GH \perp HI\), \(HI \perp IJ\), \(IJ \perp JG\), \(JG \perp GH\)) and opposite sides equal. Here, \(GH = HI = IJ = JG = 19\), so opposite sides are equal, and all angles are right angles, so it is a rectangle.
3. Rhombus: A quadrilateral with all sides equal. Here, \(GH = HI = IJ = JG = 19\), so all sides are equal, making it a rhombus.
4. Square: A quadrilateral with all sides equal and all angles right angles. Since it is a rhombus (all sides equal) and a rectangle (all angles right angles), it is a square.
5. Parallelogram: A quadrilateral with opposite sides parallel. In a rectangle (which this is), opposite sides are parallel, so it is a parallelogram.
6. Trapezoid: A trapezoid has at least one pair of parallel sides. However, this figure has two pairs of parallel sides (since it's a parallelogram), but a trapezoid is typically defined as having exactly one pair (in some definitions) or at least one pair (in others). But since it's a parallelogram (with two pairs), it doesn't fit the "exactly one pair" definition, so it is not a trapezoid.

Answer:

Quadrilateral, Parallelogram, Rectangle, Rhombus, Square