5
AssignmentMultiple Select

Symmetry

Question 5 • CA-Common Core Geometry DVHS Sem. 1

Which statements are true? Check all that apply.

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 every figure with point symmetry has rotational symmetry; A is true. A parallelogram’s diagonals bisect each other, making their intersection a center of 180° rotational symmetry, so D is true. A triangle cannot match itself after a 180° rotation, so E is true. B is false because a figure can have rotational symmetry at another angle, such as an equilateral triangle’s 120° rotation, without having point symmetry; C is false because point symmetry does not require four lines of reflectional symmetry.

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