Question

consider the original squares interior angle measures. all the interior angles measure 90°. do the interior angle measures remain the same after:
yes no any horizontal or vertical reflection?
yes no any horizontal or vertical translation?
yes no any rotation?
consider the original squares side lengths. do the side lengths remain the same after:

Explanation:

Step1: Properties of reflection

Reflection (horizontal or vertical) is a rigid transformation. Rigid transformations preserve the shape and size of a figure. Since the original square has interior angles of \(90^{\circ}\), after reflection, the interior angles remain \(90^{\circ}\).

Step2: Properties of translation

Translation (horizontal or vertical) is also a rigid transformation. It just moves the figure without changing its shape or size. So, the interior angles of the square (which were \(90^{\circ}\) originally) stay \(90^{\circ}\) after translation.

Step3: Properties of rotation

Rotation is a rigid transformation. When we rotate a square (by any angle, but in the context of a square, common rotations are by \(90^{\circ},180^{\circ},270^{\circ}\) etc. around its center), the shape and size of the square are preserved. Thus, the interior angles (which measure \(90^{\circ}\) in the original square) remain \(90^{\circ}\) after rotation.

Answer:

For "Any horizontal or vertical reflection": Yes.
For "Any horizontal or vertical translation": Yes.
For "Any rotation": Yes.