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Question

An isosceles trapezoid's top and bottom sides are marked by arrows. Its left and right sides are marked by 3 tick marks. The top base's angles are marked by 2 arcs. The bottom base's angles are marked by singular arcs.

Determine the degree of rotation that would turn the figure onto itself.

(1 point)
A rotation of
°
would turn the figure onto itself.

Answer 1

To determine the degree of rotation that would turn the isosceles trapezoid onto itself, we observe the symmetry of the figure.

An isosceles trapezoid has reflective symmetry along its vertical axis (the line that bisects the two bases). Additionally, due to its shape, it also has rotational symmetry.

For an isosceles trapezoid, the degrees that allow it to map onto itself through rotation can be found as follows:

1. An isosceles trapezoid can be rotated 180 degrees, which would place each base over the other and maintain congruence in shape.
2. In some cases, a 360 degrees rotation brings the trapezoid onto itself, but this is trivial as it does not change its position.

The only meaningful rotation that results in the trapezoid appearing the same (not just returning to the original position) is 180 degrees.

Therefore, a rotation of 180° would turn the figure onto itself. Thus the answer is:

180°.