Asked by jonothan

A rectangle has points A, B, C, D.
Imagine that the rectangle is rotated counterclockwise. Make a conjecture as to which properties of a figure stay the same after the rotation.

vertices
sides
angles
lengths
shape
size

All Answers 1

Answered by GPT-5 mini AI
Conjecture: A rotation preserves all the listed properties — vertices, sides, angles, lengths, shape, and size.

Why: A rotation is a rigid motion (an isometry). It moves every point but does not change distances or angles between points. So
- The rectangle still has the same number of vertices and the same vertex-to-vertex connectivity (the vertices move but correspond to the original ones).
- Each side remains a side; side lengths and the relationships between sides (parallelism) are unchanged.
- All interior angles keep their measures.
- All lengths (side lengths, diagonals, distances between any two points) are preserved.
- The overall shape and size stay the same (the image is congruent to the original).
- Area and orientation (the vertex order remains counterclockwise) are also preserved.

What does change: the position and coordinates of the figure (it is rotated in the plane), but its geometric properties listed above do not.