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

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.

When a Geometrical shape is rotated through certain angle

1. Shape and size will not change, that is the two rectangles will be congruent.

2. Length of sides remain same.

3. Each angle of rectangle after rotation  (image)  will be equal to rectangle before rotation (Pre image).

4. Order of vertices changes.You can say it as if pre image was ABCD , then Image can be DABC or CDBA.

5. Length →breadth, and Breadth → Length.(after one rotation,either clockwise or Anticlockwise),so lengths will change.

6.Similarly sides change after a rotation,because . Length →breadth, and Breadth → Length

The properties of rectangle that will remain same are

1. Angles

2. Shape

3. Size