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Through what different angles should a r...

Through what different angles should a rectangle be rotated to be in symmetrical position with the original position?

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To determine the different angles through which a rectangle can be rotated to be in a symmetrical position with its original position, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding Rectangle Properties**: A rectangle has opposite sides that are equal and four right angles (90 degrees). This symmetry is crucial for understanding how it can be rotated. **Hint**: Remember that the properties of a rectangle include equal opposite sides and right angles. 2. **Identifying Rotation Angles**: We need to find angles at which the rectangle will look the same as it did in its original position. The key angles to consider are multiples of 90 degrees. **Hint**: Think about how many times you can rotate a rectangle by 90 degrees before it looks the same again. 3. **First Rotation (90 degrees)**: When we rotate the rectangle 90 degrees clockwise, the rectangle will change its position but will still have the same dimensions and shape. However, it will not be in the original position. **Hint**: Visualize the rectangle on a coordinate plane to see how it changes with a 90-degree rotation. 4. **Second Rotation (180 degrees)**: If we rotate the rectangle by 180 degrees, it will look the same as the original position. This is because each corner will have moved to the position of the opposite corner. **Hint**: Consider how the corners of the rectangle move when you rotate it 180 degrees. 5. **Third Rotation (270 degrees)**: If we rotate the rectangle by 270 degrees (or 90 degrees counterclockwise), it will again look the same as the original position. **Hint**: Remember that 270 degrees is equivalent to -90 degrees, which is a counterclockwise rotation. 6. **Final Rotation (360 degrees)**: Finally, if we rotate the rectangle by 360 degrees, it will also be in the original position, as it has completed a full rotation. **Hint**: A full rotation (360 degrees) will always bring any shape back to its original position. ### Conclusion: The different angles through which a rectangle can be rotated to be in a symmetrical position with its original position are: - 0 degrees (no rotation) - 180 degrees - 360 degrees Thus, the rectangle can be rotated at angles of 0 degrees, 180 degrees, and 360 degrees to remain symmetrical with its original position.
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