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Symmetry

Question 6 • CA-Common Core Geometry DVHS Sem. 1

Which statements are true? Check all that apply.If a figure has point symmetry, it also must have rotational symmetry.If a figure has rotational symmetry, it also must have point symmetry.If a figure has point symmetry, it also must have 4-fold reflectional symmetry.All parallelograms have point symmetry.A triangle never has point symmetry.

Answer
A
If a figure has point symmetry, it also must have rotational symmetry.
B
If a figure has rotational symmetry, it also must have point symmetry.
C
If a figure has point symmetry, it also must have 4-fold reflectional symmetry.
D
All parallelograms have point symmetry.
E
A triangle never has point symmetry.

Explanation

Point symmetry means a figure matches itself after a 180° rotation, so any figure with point symmetry has rotational symmetry (A). Every parallelogram has point symmetry about the intersection of its diagonals, which makes D true. A triangle cannot match itself after a 180° rotation, so E is true. Rotational symmetry alone does not guarantee point symmetry: for example, an equilateral triangle matches after a 120° rotation but not after a 180° rotation. Thus B is false, and point symmetry does not require four-fold reflectional symmetry, so C is false.

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