Question

choose all answers that describe the polygon ghij if gh = 15, hi = 17, ij = 15, jg = 17, m∠g = m∠i, m∠h = m∠j, \\(\overline{gh} \parallel \overline{ij}\\), and \\(\overline{hi} \parallel \overline{jg}\\). answer attempt 2 out of 10 parallelogram quadrilateral rectangle rhombus square trapezoid

Explanation:

Step1: Identify polygon type by sides

The figure has 4 vertices (G, H, I, J), so it is a quadrilateral.

Step2: Check parallel side pairs

Given $\overline{GH} \parallel \overline{IJ}$ and $\overline{HI} \parallel \overline{JG}$: a quadrilateral with two pairs of parallel sides is a parallelogram.

Step3: Eliminate other classifications

• Rectangle: Requires 4 right angles; no info about right angles given, so eliminate.
• Rhombus/Square: Require all sides equal; $GH=15

eq HI=17$, so eliminate.

• Trapezoid: Defined as having only one pair of parallel sides; this has two pairs, so eliminate.

Answer:

Parallel, Quadrilateral