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Axis of Symmetry: Definitions and Examples

Symmetry is an important concept in mathematics and geometry, and refers to the idea that an object or figure is the same on both sides of a central point, line, or plane. The axis of symmetry is the central point, line, or plane around which an object or figure is symmetrical. In other words, the axis of symmetry is the line that divides an object or figure into two halves that are mirror images of each other.

There are several types of symmetry that can occur in two-dimensional shapes and figures, including rotational symmetry, reflectional symmetry, and translational symmetry. In rotational symmetry, also known as radial symmetry, an object or figure is symmetrical around a central point, and can be rotated about that point to produce a series of congruent images. In reflectional symmetry, also known as line symmetry or mirror symmetry, an object or figure is symmetrical across a central line, and can be reflected across that line to produce a congruent image. In translational symmetry, an object or figure is symmetrical with respect to a translation or shift in position, and can be moved without changing its overall shape.

Here are five examples of objects and figures with axis of symmetry:

1. Circle: A circle is a two-dimensional shape with rotational symmetry around its center point, which is also its axis of symmetry. If you were to draw a line through the center of a circle and divide it into two halves, the two halves would be congruent and symmetrical.
2. Square: A square is a two-dimensional shape with four lines of reflectional symmetry, or mirror symmetry, which intersect at its center point, which is also its axis of symmetry. If you were to draw a line through the center of a square and divide it into two halves, the two halves would be congruent and symmetrical.
3. Rectangle: A rectangle is a two-dimensional shape with two lines of reflectional symmetry, or mirror symmetry, which intersect at its center point, which is also its axis of symmetry. If you were to draw a line through the center of a rectangle and divide it into two halves, the two halves would be congruent and symmetrical.
4. Equilateral triangle: An equilateral triangle is a two-dimensional shape with three lines of reflectional symmetry, or mirror symmetry, which intersect at its center point, which is also its axis of symmetry. If you were to draw a line through the center of an equilateral triangle and divide it into two halves, the two halves would be congruent and symmetrical.
5. Rhombus: A rhombus is a two-dimensional shape with four lines of reflectional symmetry, or mirror symmetry, which intersect at its center point, which is also its axis of symmetry. If you were to draw a line through the center of a rhombus and divide it into two halves, the two halves would be congruent and symmetrical.

Quiz:

1. What is the central point, line, or plane around which an object or figure is symmetrical?
2. What are the three types of symmetry that can occur in two-dimensional shapes and figures?
3. Is a circle a two-dimensional shape with rotational symmetry or reflectional symmetry?
4. Does a square have four lines of rotational symmetry or reflectional symmetry?
5. Does a rectangle have two lines of rotational symmetry or reflectional symmetry?
6. Does an equilateral triangle have three lines of rotational symmetry or reflectional symmetry?