Question

choose all answers that describe the quadrilateral opqr if \\(\overline{op} \parallel \overline{qr}\\), \\(\overline{pq} \parallel \overline{ro}\\), and diagonals have equal length: \\(oq = pr\\).

answer attempt 1 out of 2

\\(\square\\) parallelogram
\\(\square\\) rectangle
\\(\square\\) rhombus
\\(\square\\) square
\\(\square\\) trapezoid

Explanation:

Step1: Identify Parallelogram

A quadrilateral with two pairs of parallel sides (\(\overline{OP} \parallel \overline{QR}\) and \(\overline{PQ} \parallel \overline{RO}\)) is a parallelogram. So "Parallelogram" applies.

Step2: Identify Rectangle

A parallelogram with equal - length diagonals is a rectangle. Since \(OQ = PR\) (diagonals are equal) and \(OPQR\) is a parallelogram, it is a rectangle.

Step3: Check Rhombus

A rhombus has diagonals that are not necessarily equal (they are perpendicular bisectors of each other). Since the diagonals here are equal, it is not a rhombus (unless it's a square, but we can't assume that from just equal diagonals and being a parallelogram).

Step4: Check Square

A square is a special case of a rectangle (and rhombus) with all sides equal and diagonals equal. We only know it's a parallelogram with equal diagonals, not that all sides are equal, so we can't conclude it's a square.

Step5: Check Trapezoid

A trapezoid has only one pair of parallel sides, but \(OPQR\) has two pairs of parallel sides, so it's not a trapezoid.

Answer:

Parallelogram, Rectangle