Question

the transformation maps δabc to δabc. which statement is true about the transformation? ○ it is isometric because not all side lengths and angle measures remained the same. ○ it is isometric because all side lengths and angle measures remained the same. ○ it is not isometric because not all side lengths and angle measures remained the same. ○ it is not isometric because all side lengths and angle measures remained the same.

Explanation:

1. Recall the definition of an isometric transformation: A transformation that preserves the distances (side lengths) and angle measures of a figure.
2. Analyze the triangles \( \triangle ABC \) and \( \triangle A'B'C' \). The markings (tick marks and angle arcs) indicate that corresponding sides are equal in length and corresponding angles are equal in measure.
3. Evaluate each option:

• Option 1: Incorrect. Isometric transformations do preserve side lengths and angle measures. Saying "not all" contradicts the definition.
• Option 2: Correct. Since all side lengths (from tick marks) and angle measures (from angle arcs) are preserved, the transformation is isometric.
• Option 3: Incorrect. The markings show all side lengths and angles are preserved, so it should be isometric.
• Option 4: Incorrect. The reasoning is contradictory (saying it's not isometric while stating all lengths/angles are preserved).

Answer:

B. It is isometric because all side lengths and angle measures remained the same.