Questions and Answers
What does it mean to carry a shape onto itself?
It means the shape has symmetry.
Name 3 types of symmetry.
Line, rotational, point.
What is line symmetry?
Symmetry where a figure can be mapped onto itself by a reflection across a line.
What is the relationship between the maximum number of lines of symmetry for a polygon and the number of sides?
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What is rotational symmetry?
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Why are 0 & 360 degrees excluded when saying a figure has rotational symmetry?
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What is the angle of rotation?
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What is the order of rotational symmetry?
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Which order implies no true rotational symmetry since a full 360 degree rotation was needed?
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What is the relationship between the order of a figure and the angle of rotation?
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What is point symmetry?
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What is a simple test to determine whether a figure has point symmetry?
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A figure with point symmetry is unchanged in appearance by a ___ degree rotation & also has ___ symmetry with order of ___.
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In point symmetry, the point of rotation is a ____ between every point & its image.
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Figures with point symmetry all have ____ orders & ____ degree rotational symmetry.
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Any figure with 2 lines of symmetry also has ____ symmetry.
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What shape has rotational symmetry but not line symmetry?
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What shape has exactly 2 lines of symmetry but no rotational symmetry?
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What shape has exactly 3 lines of symmetry?
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What 3 shapes have exactly 1 line of symmetry?
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What do you notice about shapes with exactly 1 line of symmetry?
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Which uppercase letters have exactly 1 line of symmetry?
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Which uppercase letters have exactly 2 lines of symmetry?
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Which uppercase letters have rotational symmetry & point symmetry?
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Which uppercase letters have no symmetry?
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Which uppercase letter has point symmetry but not rotational symmetry?
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Study Notes
Symmetry in Geometry
- Symmetry means a shape can be carried onto itself through specific transformations.
- Types of symmetry include line symmetry, rotational symmetry, and point symmetry.
Line Symmetry
- Line (or reflectional) symmetry occurs when a figure maps onto itself by reflection across a line.
- The maximum number of lines of symmetry in a polygon equals the number of its sides.
Rotational Symmetry
- A figure has rotational symmetry if it can be rotated around a point and coincide with itself at any angle between 0 and 360 degrees.
- Zero and 360 degrees are excluded from consideration as they represent the starting position.
- The angle of rotation is the smallest angle needed for a figure to coincide with itself and is always a factor of 360.
- The order of rotational symmetry indicates the number of positions where a figure looks the same after rotation.
Relationships and Orders
- An order 1 indicates no true rotational symmetry as it requires a full 360-degree rotation to appear unchanged.
- The relationship between order and angle of rotation is expressed as order multiplied by angle equating to 360 degrees.
Point Symmetry
- Point symmetry involves every point of a shape having a matching point the same distance from a central point but in the opposite direction.
- A simple test for point symmetry is to turn the figure upside down and observe if it looks the same.
- Figures with point symmetry maintain appearance under a 180-degree rotation and have order 2 rotational symmetry.
Characteristics of Figures
- In point symmetry, the point of rotation is the midpoint between every point and its image.
- Figures with point symmetry typically have even orders and 180-degree rotational symmetry.
- Any figure possessing two lines of symmetry also has point symmetry.
Classification of Shapes
- Parallelograms have rotational symmetry but lack line symmetry.
- Rectangles display exactly two lines of symmetry but no rotational symmetry.
- Equiangular or equilateral triangles have three lines of symmetry.
- Isosceles triangles, isosceles trapezoids, and kites each have one line of symmetry.
Symmetry in Letters
- Uppercase letters with exactly one line of symmetry include A, B, C, D, E, K, M, T, U, V, W, and Y.
- Uppercase letters with exactly two lines of symmetry are H, I, O, and X.
- Letters with both rotational and point symmetry include H, I, N, O, S, X, and Z.
- Letters lacking any symmetry at all are F, G, J, L, P, Q, and R.
- The letter Y exhibits point symmetry but does not possess rotational symmetry.
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Test your knowledge of symmetry in geometry with these flashcards. Explore key concepts such as types of symmetry, definitions, and properties of shapes. Perfect for students who want to strengthen their understanding of geometric principles.
