To evaluate the statements about the picture frame after it is rotated 180 degrees clockwise about its center, we need to consider the properties of geometric figures and their relationships after such a rotation.
- When a shape is rotated 180 degrees around its center:
- Each point of the shape moves to a position directly across from it, maintaining the same distance from the center.
- Parallel sides remain parallel.
- The measurements of the sides do not change.
Analysis of Each Statement:
A. Side WX would be parallel to Side WZ, and Side WX would measure 6 inches.
- We need to establish if WX is indeed parallel to WZ and if its measurement aligns with the frame's properties. Without the diagram, it's hard to validate this specific relationship.
B. Side WX would be parallel to Side ZY, and Side ZY would measure 12 inches.
- Similar to A, we assess WX's relationship with ZY post-rotation. Again, the lack of visual has us unable to affirm this.
C. Side WZ would be parallel to Side XY, and Side WZ would measure 8 inches.
- If side WZ is parallel to XY before rotation, it would remain parallel after, but we can't confirm the length without context.
D. Side WZ would be perpendicular to Side XY, and Side XY would measure 10 inches.
- Perpendicular relationships would hold post-rotation as long as they were perpendicular initially.
Conclusion:
Without visual data, one cannot definitively ascertain the true statements based solely on the provided options. However, the correct approach would be to confirm the original relationships of the sides involved.
If we assume WZ and XY are perpendicular (which is common in rectangular frames), then D could potentially be true. Still, verification hinges on the actual frame layout.
Thus, based on logical reasoning without the visual aid, D seems the most likely statement to be true provided WZ and XY are actually perpendicular initially, and none of the other sides contradict the frame's characteristics.
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