Use the image to answer the question.

The image is a diagram showing an isosceles trapezoid with marked congruent sides and angles.

The image contains a geometric shape, specifically an isosceles trapezoid. The trapezoid is drawn with bold black lines. The top base is marked with arrows indicating parallel lines. The two non-parallel sides are marked with three short, parallel orange lines, indicating they are of equal length. The bottom base is also marked with an arrow, indicating it is parallel to the top base. The two base angles on the left and right side are marked with arcs of blue indicating congruence. The two angles at the top are marked with concentric green arcs, demonstrating their congruence. The overall atmosphere is neutral and purely mathematical; there is no emotional context or implied mood beyond the technical information presented for geometric analysis.

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

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

it isn't 180 imbecile

1 answer

To determine the degree of rotation that would turn an isosceles trapezoid onto itself, we need to consider its symmetry.

An isosceles trapezoid has a line of symmetry that passes through the midpoints of the two bases and the vertices of the non-parallel sides. It is symmetric with respect to this vertical line.

Rotation by 180°: This would not map the trapezoid onto itself as each base and side would not match up.
Rotation by 360°: This brings it back to the original position, but it is not a useful answer for our case.
Rotation by 0°: This technically does map it onto itself but typically isn’t considered as a valid non-trivial rotation.

Thus, the smallest non-trivial rotation that leaves the trapezoid looking the same is not 180°; it’s simply:

A rotation of 180° about the center does actually map it back to itself:

The answer is: A rotation of 180° would turn the figure onto itself.

If the answer isn't accepted then please provide its exact invalidation.