Question

which graph demonstrates a transformation that preserves both distance and angle measure? (1 point)

Explanation:

Step1: Recall rigid - motion definition

Rigid motions preserve distance and angle measure.

Step2: Analyze the graph

Check if side - lengths and angle - measures of $\triangle ABC$ and $\triangle A'B'C'$ are equal. If they are, it's a rigid motion.

Answer:

Transformations that preserve both distance and angle - measure are called rigid - motions. Examples of rigid - motions include translations, rotations, and reflections. In the given graph, if the transformation from $\triangle ABC$ to $\triangle A'B'C'$ shows that the lengths of the sides and the measures of the angles are the same, it is a rigid - motion. Without seeing all the options, if the transformation from $\triangle ABC$ to $\triangle A'B'C'$ has congruent side - lengths and congruent angle - measures, then this graph represents a rigid transformation. However, if we assume this is the only graph and it is a valid rigid transformation: The graph shows a transformation where the shape and size of the triangle are maintained. So, if this is a translation, rotation, or reflection (which can be verified by checking side - lengths and angle - measures), this graph demonstrates a transformation that preserves both distance and angle measure.