Triangle ABC is transformed to create triangle MNL. 2 triangles have identical side lengths and measures. The second triangle is shifted down and slightly to the right. Which statement is true? The transformation is rigid because corresponding side lengths and angles are congruent. The transformation is rigid because corresponding side lengths are congruent and corresponding angles are not congruent. The transformation is nonrigid because the two triangles have different names. The transformation is nonrigid because the three sides and the three angles in each triangle have different measures.

Answer: The transformation is rigid because corresponding side lengths and angles are congruent. When a figure is transformed into another figure and their sizes and shapes remain exactly the same, we say the transformation is rigid. A rigid transformation does not alter the figure's side lengths or angle measures. Given that triangles ABC and MNL have identical side lengths and angle measures, we can conclude that the transformation undergone by triangle ABC to become triangle MNL is indeed rigid. The shift down and slightly to the right is described as a translation which is a type of rigid transformation.

Extra: In geometry, transformations can change the position and orientation of a shape but not its size or form. There are typically four types of transformations:

1. Translation: Moving a shape up, down, or to the side without rotating or flipping it. 2. Rotation: Turning the figure around a fixed point without changing its size or shape. 3. Reflection: Flipping a figure over a line so it creates a mirror image. 4. Dilation: Making the figure larger or smaller while maintaining the shape's proportions. Note that dilation is not a rigid transformation because it changes the size of the figure.

The property of rigidity ensures that all corresponding sides and angles remain congruent (equal in measure) before and after the transformation. This principle is fundamental to the concept of congruence in geometry where two shapes are said to be congruent if one can be transformed into the other using a series of rigid transformations. The final option stating that the transformation is nonrigid because the two triangles have different names is not geometrically relevant; names do not affect the properties of the shapes.