GEOMETRY (HOLT 9 -5) K . SANTOS

Symmetry

Symmetry

A figure has symmetry if there is a transformation (change) of the figure such that the image coincides with the preimage (original image)

Can you fold it onto itself exactly? Can you rotate it without anyone knowing?

There are two types of symmetry:Reflectional Symmetry----foldingRotational Symmetry------spinning/rotating

Reflectional Symmetry (line symmetry)

A figure has reflectional symmetry (line symmetry) if it can be reflected across a line so that the image coincides with the preimage.

Fold the figure along the line of symmetry and the halves match up exactly

Reflectional Symmetry—one half of the image is a mirror image of its other half

The line of symmetry (axis of symmetry) divides the figure into two congruent halves.

Examples of Figures with Reflectional Symmetry

Examples of Letters with Reflectional Symmetry

HELLO MATH STUDENTS!

Letters with reflectional (line) symmetry: H, E, O, M, A, T, U, D

HELLO MATH STUDENTS!

Letters with reflectional (line) symmetry:H, E, O, T, D

Rotational Symmetry (Radial Symmetry)

A figure that has rotational symmetry if it can be rotated about a point by an angle greater than 0 and less than 360 so that the image coincides with the preimage.

Can rotate or spin a figure around and can’t even tell the figure has been moved

Full circle is 360 -- if this is the only rotation possible then the figure does not have rotational symmetry

The angle of rotational symmetry is the smallest angle through which a figure can be rotated to coincide with itself

The number of times the figure coincides with itself as it rotates 360 is called the order of the rotational symmetry

Examples of Figures with Rotational Symmetry

(360) ¼(360) 180 every 90 order: 2 order: 4

1/3(360) 1/5 (360) every 120 every 72 order: 3 order: 5

Examples of Figures with Rotational Symmetry

½(360) ¼(360) 1/12(360)180 every 90 every 30Order: 2 order: 4 order: 12

has rotational symmetry for any degree from 0 to 360

Point Symmetry

Has rotational symmetry of exactly 180Can turn a figure upside down