Math  /  Geometry

QuestionWhat types of symmetry, if any, does the following figure have? none point symmetry only line and rotational symmetry point and rotational symmetry

Studdy Solution

STEP 1

1. The figure in question is a parallelogram.
2. The diagonal line and center point are part of the symmetry analysis.
3. We are considering line symmetry, rotational symmetry, and point symmetry.

STEP 2

1. Analyze line symmetry.
2. Analyze rotational symmetry.
3. Analyze point symmetry.
4. Determine the types of symmetry present.

STEP 3

Analyze line symmetry:
A figure has line symmetry if it can be reflected over a line and appear unchanged. In a parallelogram, the only potential lines of symmetry are the diagonals. However, reflecting over a diagonal does not map the parallelogram onto itself because opposite sides are not equal in length. Therefore, a parallelogram does not have line symmetry.

STEP 4

Analyze rotational symmetry:
A figure has rotational symmetry if it can be rotated (less than a full circle) about a central point and appear unchanged. A parallelogram can be rotated 180180^\circ about its center and appear unchanged. Thus, a parallelogram has rotational symmetry of order 2.

STEP 5

Analyze point symmetry:
A figure has point symmetry if every part of the figure has a matching part at an equal distance from a central point but in the opposite direction. A parallelogram has point symmetry about its center because it can be rotated 180180^\circ and appear unchanged, which is equivalent to having point symmetry.

STEP 6

Determine the types of symmetry present:
Based on the analysis, the parallelogram has rotational symmetry and point symmetry, but not line symmetry.
The types of symmetry present are:
point and rotational symmetry \boxed{\text{point and rotational symmetry}}

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