Question

1. choose all answers that describe the polygon rstu if rs = 23, st = 41, tu = 23, ur = 41, \\( \overline { r s } \perp \overline { s t } \\), \\( \overline { s t } \perp \overline { t u } \\), \\( t u \perp u r \\), and \\( \overline { u r } \perp \overline { r s } \\).

parallelogram quadrilateral rectangle
rhombus square

Explanation:

Step1: Analyze the number of sides

A quadrilateral has 4 sides. The polygon \(RSTU\) has 4 sides (\(RS\), \(ST\), \(TU\), \(UR\)), so it is a quadrilateral.

Step2: Check parallel - side property

In a parallelogram, opposite sides are equal. Here, \(RS = TU=23\) and \(ST = UR = 41\). Also, since \(\overline{RS}\perp\overline{ST}\), \(\overline{ST}\perp\overline{TU}\), \(\overline{TU}\perp\overline{UR}\), and \(\overline{UR}\perp\overline{RS}\), the adjacent sides are perpendicular. In a parallelogram with right - angles is a rectangle.

A rhombus has all sides equal. Here \(RS = 23\) and \(ST=41\), so it is not a rhombus. A square has all sides equal. Since \(RS
eq ST\), it is not a square.

Answer:

Parallelogram, Quadrilateral, Rectangle