Symmetries of an Equilateral Triangle

Click on the option at the right and find the meaning of the symbols (12), (13), (23), (123), (132) and (1) with reference to the symmetries if an equilateral triangle 123. Click to the square boxes in the right of the following figure.

What does (23) mean?

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A
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 1.
B
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 2.
C
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 3.
D
rotation of the triangle about the center at the point that is the centroid of the triangle by 120 degrees.
E
rotation of the triangle about the center at the point that is the centroid of the triangle by 240 degrees.
F
rotation of the triangle about the center at the point that is the centroid of the triangle by 360 degrees.

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What does (13) mean?

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A
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 1.
B
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 2.
C
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 3.
D
rotation of the triangle about the center at the point that is the centroid of the triangle by 120 degrees.
E
rotation of the triangle about the center at the point that is the centroid of the triangle by 240 degrees.
F
rotation of the triangle about the center at the point that is the centroid of the triangle by 360 degrees.

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What does (12)?

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A
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 1.
B
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 2.
C
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 3.
D
rotation of the triangle about the center at the point that is the centroid of the triangle by 120 degrees.
E
rotation of the triangle about the center at the point that is the centroid of the triangle by 240 degrees.
F
rotation of the triangle about the center at the point that is the centroid of the triangle by 360 degrees.

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What does (123) mean?

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A
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 1.
B
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 2.
C
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 3.
D
rotation of the triangle about the center at the point that is the centroid of the triangle by 120 degrees.
E
rotation of the triangle about the center at the point that is the centroid of the triangle by 240 degrees.
F
rotation of the triangle about the center at the point that is the centroid of the triangle by 360 degrees.

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What does (132)?

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A
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 1.
B
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 2.
C
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 3.
D
rotation of the triangle about the center at the point that is the centroid of the triangle by 120 degrees.
E
rotation of the triangle about the center at the point that is the centroid of the triangle by 240 degrees.
F
rotation of the triangle about the center at the point that is the centroid of the triangle by 360 degrees.

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What does (1)= (1)(2)(3) mean?

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A
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 1.
B
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 2.
C
reflection of the triangle in the line that is the median of the triangle 123 through the vertex 3.
D
rotation of the triangle about the center at the point that is the centroid of the triangle by 120 degrees.
E
rotation of the triangle about the center at the point that is the centroid of the triangle by 240 degrees.
F
rotation of the triangle about the center at the point that is the centroid of the triangle by 360 degrees.

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Symmetries of an Equilateral Triangle

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