Which statement about the transformation is true?
A It is rigid because all side lengths and angles are congruent.
B It is rigid because no side lengths or angles are congruent.
C It is nonrigid because all side lengths are congruent.
D It is nonrigid because no side lengths or angles are congruent.
The correct answer and explanation is :
The correct answer is: A. It is rigid because all side lengths and angles are congruent.
Explanation (300 words):
In geometry, a transformation refers to a change in the position, size, or shape of a figure. There are two main categories of transformations: rigid and nonrigid.
A rigid transformation (also called an isometry) preserves the size and shape of a figure. That means the lengths of the sides and the measures of the angles in the figure stay exactly the same after the transformation. Examples of rigid transformations include:
- Translation: sliding a shape without rotating or flipping it.
- Rotation: turning a shape around a fixed point.
- Reflection: flipping a shape over a line (mirror image).
Under these rigid motions, the image (new figure) is congruent to the original figure. “Congruent” means that all corresponding sides and angles are equal in measure.
In contrast, a nonrigid transformation changes the size or proportions of the shape. This includes transformations like:
- Dilation: resizing a figure larger or smaller from a center point.
- Shearing or stretching: distorting the figure’s shape.
In nonrigid transformations, the image is not congruent to the original figure because either side lengths, angles, or both change.
Now, let’s examine the answer choices:
- Choice A states the transformation is rigid because all side lengths and angles are congruent—this matches the definition of a rigid transformation and is correct.
- Choice B contradicts itself: it claims rigidity but says no sides or angles are congruent.
- Choice C says it’s nonrigid even though all sides are congruent—but ignores the angles, which matter too.
- Choice D is only correct if the transformation changed both side lengths and angles—but that would be nonrigid, not rigid.
Therefore, Choice A correctly describes a rigid transformation.