3. Are all rotations considered a rigid motion? Explain why or why not by explaining its effects on a figure's angles and line segments.
Answer
\(\boxed{\text{Yes, all rotations are considered a rigid motion because they preserve the lengths of line segments and the measures of angles in a figure.}}\)
Step 1 ：This question is asking about the properties of rigid motions, specifically rotations. A rigid motion is a transformation that preserves distance and angle measures. Therefore, to answer this question, we need to consider whether a rotation changes the distance between points (the lengths of line segments) or the measures of angles in a figure.
Step 2 ：A rotation is a type of transformation where an object is rotated around a point (the center of rotation). The distance from any point in the object to the center of rotation remains constant. Therefore, the lengths of line segments in the object do not change. Similarly, because the object is simply being 'spun around', the angles within the object do not change either.
Step 3 ：Therefore, a rotation is a rigid motion because it preserves distance and angle measures.
Step 4 ：\(\boxed{\text{Yes, all rotations are considered a rigid motion because they preserve the lengths of line segments and the measures of angles in a figure.}}\)
