To evaluate the statements about the window's design comprising six pieces of glass (A, B, C, D, E, and F), let's analyze each option based on the transformations described:
A. The angle rotation from a horizontal axis to the tip of each piece is the same.
This statement may or may not be true depending on the specific angles after rotations and reflections. Without additional information about angles, we cannot confirm this as true.
B. The perimeter of each piece is the same.
This statement could be true if each piece is created from transformations of the original piece A. However, this depends on the nature of the transformations. If rotations and reflections maintain the dimensions of piece A, then this could be correct, but without specific information, it's uncertain.
C. Each piece (B through F) is a translation of piece A.
This statement is false. Translations involve shifting a shape without altering its orientation or size, while the described process includes rotations and a reflection, which change the orientation of the shapes from piece A.
D. Piece A and piece D are the only congruent shapes.
While piece A is the original, piece D is formed by reflecting piece A, which could result in congruent shapes under certain transformations, depending on the specific design. Therefore, this statement can potentially be true if reflections preserve congruence in this context.
Given these assessments, the most likely true statement that can be determined based on geometric transformations is:
D. Piece A and piece D are the only congruent shapes.
This is because piece D is derived from piece A through reflection, which typically preserves congruence, while the other pieces B, C, E, and F may not maintain that distinction depending on their transformations.
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