Question

determining a figure based on reflectional and rotational symmetry
which polygon will always have 4 - fold reflectional symmetry and order 4 rotational symmetry?
rectangle
trapezoid
right triangle
square

Explanation:

• Rectangle: Has 2 - fold reflectional symmetry (vertical and horizontal axes) and order 2 rotational symmetry (rotating \(180^{\circ}\) about the center maps the rectangle onto itself).
• Trapezoid: In general, a trapezoid (non - isosceles) has no reflectional symmetry. An isosceles trapezoid has 1 - fold reflectional symmetry (the axis of symmetry is the line perpendicular to the bases and passing through the mid - points of the non - parallel sides) and order 1 rotational symmetry (only the identity rotation \(0^{\circ}\) maps it onto itself).
• Right triangle: In general, a right triangle has no reflectional symmetry (except for an isosceles right triangle which has 1 - fold reflectional symmetry). And it has order 1 rotational symmetry.
• Square:
• Reflectional symmetry: A square has 4 lines of reflectional symmetry. Two are the lines joining the mid - points of opposite sides (horizontal and vertical), and two are the diagonals.
• Rotational symmetry: When rotated by \(90^{\circ}\), \(180^{\circ}\), \(270^{\circ}\), and \(360^{\circ}\) about its center, it maps onto itself. So, it has order 4 rotational symmetry.

Answer:

square