Question

select all the figures with 180° rotation symmetry.

Explanation:

• For Figure A: A right - angled triangle (non - isosceles) does not have \(180^{\circ}\) rotation symmetry. When rotated \(180^{\circ}\), it will not map onto itself.
• For Figure B: A rectangle has \(180^{\circ}\) rotation symmetry. The center of the rectangle is the center of rotation. When rotated \(180^{\circ}\) about its center, each vertex is mapped to the opposite vertex, and the sides are mapped to the opposite sides.
• For Figure C: A square (a special case of a rectangle) has \(180^{\circ}\) rotation symmetry. Rotating it \(180^{\circ}\) about its center (the intersection of its diagonals) maps each vertex to the opposite vertex and each side to the opposite side.
• For Figure D: A non - regular pentagon does not have \(180^{\circ}\) rotation symmetry. A regular pentagon has rotational symmetry of order \(5\) (\(72^{\circ},144^{\circ},216^{\circ},288^{\circ},360^{\circ}\)), and a non - regular pentagon will not map onto itself when rotated \(180^{\circ}\).
• For Figure E: A regular hexagon has \(180^{\circ}\) rotation symmetry. The center of the hexagon is the center of rotation. When rotated \(180^{\circ}\) about its center, each vertex is mapped to the opposite vertex, and each side is mapped to the opposite side.

Answer:

B. Rectangle, C. Square, E. Regular hexagon