Question

1. select the shape that has 180 degree rotational symmetry.

a. rhombus
b. trapezoid
c. isosceles trapezoid
d. quadrilateral

Explanation:

A rhombus has 180 - degree rotational symmetry because rotating it by 180 degrees about its center maps it onto itself. A trapezoid (in general) and an isosceles trapezoid have rotational symmetry of 180 degrees? Wait, no, an isosceles trapezoid has 180 - degree rotational symmetry? Wait, no, actually, a rhombus: when you rotate a rhombus 180 degrees around its center, the vertices swap in a way that the shape coincides with the original. A general trapezoid does not have 180 - degree rotational symmetry. An isosceles trapezoid has 180 - degree rotational symmetry? Wait, no, let's recall: rotational symmetry means that when you rotate the figure by a certain angle (less than 360), it looks the same. A rhombus: yes, because its diagonals bisect each other at the center, so rotating 180 degrees swaps opposite vertices and opposite sides, and it matches. A trapezoid (non - isosceles) has no rotational symmetry. An isosceles trapezoid: when rotated 180 degrees, does it map onto itself? Let's see, the top base and bottom base are parallel and equal in an isosceles trapezoid? No, the top and bottom bases are of different lengths. Wait, no, in an isosceles trapezoid, the legs are equal, and the base angles are equal. If we rotate it 180 degrees about the center (the midpoint between the midpoints of the two bases), then the top base would swap with the bottom base, but since they are of different lengths, it would not coincide. Wait, I made a mistake earlier. A rhombus: all sides are equal, and the diagonals bisect each other at 90 degrees? No, the diagonals of a rhombus bisect the angles and bisect each other. When you rotate a rhombus 180 degrees around the intersection point of its diagonals, each vertex is mapped to the opposite vertex, and since the sides are equal and the angles are equal, the shape coincides with the original. So a rhombus has 180 - degree rotational symmetry. A trapezoid (general) does not. An isosceles trapezoid: let's check, if we rotate it 180 degrees, the left leg would go to the right leg's position, but since the bases are of different lengths, it won't match. A quadrilateral is a general four - sided figure, most don't have 180 - degree rotational symmetry. So the correct answer is A.

Answer:

A. Rhombus