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What is the order of symmetry for a shape that coincides with itself after a 180-degree rotation?
- a)90 degrees
- b)120 degrees
- c)180 degrees
- d)360 degrees
Correct answer is option 'C'. Can you explain this answer?
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What is the order of symmetry for a shape that coincides with itself a...
The order of symmetry for a shape that coincides with itself after a 180-degree rotation is 180 degrees. In other words, the shape looks the same after rotating it by 180 degrees.
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What is the order of symmetry for a shape that coincides with itself a...
Understanding Symmetry
Symmetry in shapes refers to the property where a shape looks the same after a certain rotation or reflection. The order of symmetry indicates how many times a shape coincides with itself during a complete 360-degree rotation.
180-Degree Rotation
When a shape matches its original position after a 180-degree rotation, it indicates that the shape has a specific kind of symmetry:
- Coinciding After Half Turn: If a shape looks the same after a 180-degree rotation, it means that for every point on the shape, there is another point directly opposite it that is equidistant from the center.
- Example: A simple example is a rectangle. When you rotate it 180 degrees, it looks the same as it did before.
Order of Symmetry Calculation
To determine the order of symmetry, we can use the formula:
- Total Degrees of Rotation: 360 degrees
- Degrees of Rotation for Coincidence: 180 degrees
The order of symmetry is calculated as follows:
- Order = 360 degrees / 180 degrees = 2
This means the shape coincides with itself 2 times during a full rotation.
Correct Answer: 180 Degrees
Thus, the correct option is c) 180 degrees. This reflects that the shape has an order of symmetry of 2, as it matches its original form after a rotation of 180 degrees. This concept is vital in understanding geometric shapes and their properties.
Symmetry in shapes refers to the property where a shape looks the same after a certain rotation or reflection. The order of symmetry indicates how many times a shape coincides with itself during a complete 360-degree rotation.
180-Degree Rotation
When a shape matches its original position after a 180-degree rotation, it indicates that the shape has a specific kind of symmetry:
- Coinciding After Half Turn: If a shape looks the same after a 180-degree rotation, it means that for every point on the shape, there is another point directly opposite it that is equidistant from the center.
- Example: A simple example is a rectangle. When you rotate it 180 degrees, it looks the same as it did before.
Order of Symmetry Calculation
To determine the order of symmetry, we can use the formula:
- Total Degrees of Rotation: 360 degrees
- Degrees of Rotation for Coincidence: 180 degrees
The order of symmetry is calculated as follows:
- Order = 360 degrees / 180 degrees = 2
This means the shape coincides with itself 2 times during a full rotation.
Correct Answer: 180 Degrees
Thus, the correct option is c) 180 degrees. This reflects that the shape has an order of symmetry of 2, as it matches its original form after a rotation of 180 degrees. This concept is vital in understanding geometric shapes and their properties.
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What is the order of symmetry for a shape that coincides with itself after a 180-degree rotation?a)90 degreesb)120 degreesc)180 degreesd)360 degreesCorrect answer is option 'C'. Can you explain this answer?
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