Question

1. choose all answers that describe the polygon

fghi if fg = gh = hi = if and
m∠f = m∠g = m∠h = m∠i.

parallelogramquadrilateral

rhombus
square
rectangle

Explanation:

Step1: Analyze the properties of a parallelogram

A parallelogram has opposite sides equal and opposite angles equal. Given \(FG = GH=HI = IF\) (all sides equal) and \(m\angle F=m\angle G=m\angle H=m\angle I\) (all angles equal). A quadrilateral is a four - sided polygon, which \(FGHI\) is. A parallelogram has opposite sides equal and opposite angles equal. Since all sides are equal (\(FG = GH=HI = IF\)), it satisfies the side - equality condition for a parallelogram (a parallelogram can have all sides equal, which is a special case).

Step2: Analyze the properties of a rhombus

A rhombus is a parallelogram with all sides equal. Here \(FG = GH=HI = IF\), so it is a rhombus.

Step3: Analyze the properties of a 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 angles are \(90^{\circ}\). So we can't confirm it's a square.

Step4: Analyze the properties of a rectangle

A rectangle is a parallelogram with all angles equal to \(90^{\circ}\). Since we don't know if the angles are \(90^{\circ}\), we can't confirm it's a rectangle.

Answer:

• Parallelogram
• Rhombus
• Quadrilateral