Question

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 (along the lines joining the mid - points of opposite sides) and order 2 rotational symmetry (rotating by \(180^{\circ}\) about the center maps the rectangle onto itself).
• Trapezoid: A non - isosceles trapezoid has no reflectional symmetry. An isosceles trapezoid has 1 - fold reflectional symmetry (along the line passing through the mid - points of the non - parallel sides) and no rotational symmetry (except for the identity rotation).
• Right triangle: Has no rotational symmetry (except for the identity rotation) and, in general, no reflectional symmetry (an isosceles right triangle has 1 - fold reflectional symmetry).
• Square:
• Reflectional symmetry: There are 4 lines of symmetry. Two lines are along the diagonals, and two lines are along the lines joining the mid - points of opposite sides. So, it has 4 - fold reflectional symmetry.
• Rotational symmetry: When rotated by \(90^{\circ},180^{\circ},270^{\circ},360^{\circ}\) about its center, it maps onto itself. So, it has order 4 rotational symmetry.

Answer:

D. square