Question

figure cdef can be translated, reflected, or rotated to form figure stuv. which statement is true?
the angle measures of figure cdef are only congruent to the corresponding angles of figure stuv for translations and reflections.
the sum of the angle measures of figure cdef are double the angle measures of figure stuv.
the area of figure cdef will be congruent to the area of figure stuv.
the perimeter of figure cdef will be less than the perimeter of figure stuv for reflections and rotations.

Explanation:

1. Recall the properties of translations, reflections, and rotations (rigid transformations): these transformations preserve the shape and size of the figure.
2. Analyze each option:

• First option: Rigid transformations (translation, reflection, rotation) all preserve angle measures, so this statement is false.
• Second option: Rigid transformations preserve angle measures, so the sum of angles will be equal, not double. This is false.
• Third option: Rigid transformations preserve area (since they preserve shape and size), so the area of CDEF and STUV will be congruent. This is true.
• Fourth option: Rigid transformations preserve side lengths, so the perimeter (sum of side lengths) will be equal, not less. This is false.

Answer:

The area of figure \( CDEF \) will be congruent to the area of figure \( STUV \).