Question

1. choose all answers that describe the polygon fghi if fg = 12, gh = 12, hi = 12, if = 12, and m∠f = m∠g = m∠h = m∠i.

□ parallelogram □ quadrilateral □ rectangle
□ rhombus □ square

Explanation:

• Quadrilateral: A polygon with four sides. Since \(FGHI\) has four sides (\(FG\), \(GH\), \(HI\), \(IF\)), it is a quadrilateral.
• Parallelogram: In a parallelogram, opposite sides are equal and parallel. Here, \(FG = HI = 12\) and \(GH=IF = 12\). Also, in a quadrilateral, if opposite angles are equal ( \(m\angle F=m\angle H\) and \(m\angle G = m\angle I\) as \(m\angle F=m\angle G=m\angle H=m\angle I\) implies opposite - angle equality), it is a parallelogram.
• Rhombus: A rhombus is a parallelogram with all sides equal. Given \(FG = GH=HI = IF = 12\), all sides are equal, so it is a rhombus.
• Square: A square is a rhombus with all angles equal to \(90^{\circ}\). We are only given that \(m\angle F=m\angle G=m\angle H=m\angle I\), but we don't know if the measure of each angle is \(90^{\circ}\).
• Rectangle: A rectangle is a parallelogram with all angles equal to \(90^{\circ}\). Since we don't know the measure of the angles (only that they are equal), we can't confirm it's a rectangle.

Answer:

Quadrilateral, Parallelogram, Rhombus