Question

choose all answers that describe the polygon stuv if ( stcong uv ), ( tucong vs ), and ( mangle s=mangle t = mangle u=mangle v ).
answer attempt 1 out of 2
parallelogram
quadrilateral
rectangle
rhombus
square
trapezoid

Explanation:

1. Quadrilateral: The polygon has 4 vertices (S, T, U, V), so it is a quadrilateral by definition (a four - sided polygon).
2. Parallelogram: A parallelogram is defined as a quadrilateral with both pairs of opposite sides congruent. Given that \(\overline{ST}\cong\overline{UV}\) and \(\overline{TU}\cong\overline{VS}\) (assuming \(VB\) is a typo and should be \(VS\)), this satisfies the opposite - sides - congruent condition for a parallelogram.
3. Rectangle: In a parallelogram, if all the angles are equal, then each angle is \(90^{\circ}\) (since the sum of interior angles of a quadrilateral is \(360^{\circ}\), and \(360\div4 = 90\) when all angles are equal). A parallelogram with four right angles is a rectangle.
4. We cannot be sure it is a rhombus or a square because we only know about the congruence of opposite sides, not all sides. A trapezoid has only one pair of parallel sides, but our figure has two pairs of congruent (and thus parallel) sides, so it is not a trapezoid.

Answer:

Quadrilateral, Parallelogram, Rectangle