Question

triangle abc is transformed to create triangle mnl. 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.

Explanation:

1. Recall the definition of a rigid transformation: A rigid transformation (also called an isometry) is a transformation that preserves the shape and size of a figure, meaning corresponding side lengths and corresponding angles are congruent.
2. Analyze each option:

• Option 1: "The transformation is rigid because corresponding side lengths and angles are congruent." - This matches the definition of a rigid transformation. The markings on the triangles (tick marks on sides and angle arcs) indicate that corresponding sides and angles are congruent, so the transformation preserves the triangle's size and shape.
• Option 2: "The transformation is rigid because corresponding side lengths are congruent and corresponding angles are not congruent." - A rigid transformation must preserve angles (make them congruent), so this is incorrect.
• Option 3: "The transformation is nonrigid because the two triangles have different names." - The name of the triangle does not determine if a transformation is rigid or nonrigid. Rigid transformations depend on preserving size and shape, not the label of the figure, so this is incorrect.
• Option 4: "The transformation is nonrigid because the three sides and the three angles in each triangle have different measures." - The markings show that corresponding sides and angles are congruent (same tick marks for sides, same arc marks for angles), so their measures are equal. Thus, this is incorrect.

Answer:

The transformation is rigid because corresponding side lengths and angles are congruent.