Which of the following transformations preserves the measures of the angles but changes the lengths of the sides of the figure?
choices?
scaling preserves angles, but changes distances
To determine which of the following transformations preserves the measures of the angles but changes the lengths of the sides of the figure, we need to understand the concept of transformations and how they affect geometric properties.
Transformations in geometry can be classified into three main types: translations, rotations, and reflections. Let's examine each one and see how they affect angles and side lengths.
1. Translation: This transformation moves an object without changing its size or shape. It preserves both angle measures and side lengths. Therefore, a translation does not change the lengths of the sides, so it does not meet the criteria.
2. Rotation: This transformation revolves an object around a fixed point called the center of rotation. A rotation can change the lengths of the sides depending on the angle of rotation and the distance from the center of rotation. As a result, a rotation does not preserve the lengths of the sides, so it does not meet the criteria.
3. Reflection: This transformation flips an object across a line called the line of reflection. A reflection preserves angle measures, but it also changes the lengths of the sides. When a figure is reflected, the distances between corresponding points on the original and reflected figures are different. As a result, a reflection satisfies the condition of preserving angle measures while changing the lengths of the sides.
Therefore, the correct answer is a reflection.