Question

Which type(s) of symmetry does the following object have?

Select all that apply.
diagonal line of symmetry
no symmetry
vertical line of symmetry
horizontal line of symmetry
rotational symmetry

Answer 1

• diagonal line
• vertical line
• horizontal line
• rotational

Explanation:

An object has a point of symmetry if that point is the midpoint between any point on the object and another point on the object.

An object has a line of symmetry if that line is a perpendicular bisector of the segment between any point on the object and another point on the object.

An object has rotational symmetry if it can be rotated about its point of symmetry through a positive angle at most 360° and become indistinguishable from the unrotated object. The number of such angles is the degree of rotational symmetry.

Applying these definitions

The given square has a point of symmetry at its center. When the object is rotated some multiple of 90° about its center, it maps to itself. It has rotational symmetry of degree 4.

Any horizontal, vertical, or diagonal line (between opposite corners) through the center of the figure will divide it into two parts that are reflections of each other across that line. This means that the figure has ...

• diagonal lines of symmetry (2)
• a vertical line of symmetry
• a horizontal line of symmetry