Question

Imagine that the rectangle is rotated counterclockwise. Make a conjecture as to which properties of a figure stay the same after the rotation.

Answer 1

a shape rotated does not change the side and angle measurements.
A rotation is an isometric transformation, isometric transformations do not change the size or shape of a figure and the side and angle measurements remain intact.

Answer 2

The rotation described in the problem is known as a rigid transformation, which refers to all transformation that doesn't change the shape or size of the object, like this case.

Basically, the rectangle after the counterclockwise rotation maintains its side lengths, its angle, but changes its vertices, that is, its coordinates without altering its dimension. This conjecture englobes all important qualities of the rectangle.

Therefore, the properties that remain the same after rotation are angles, sides and shape.