Honors Geometry Blue Unit

Vocabulary

Rigid Motion

a movement where an object stays the same shape and size

Transalation

A rigid motion where an object “slides” in the same direction without changing its size or shape.

Rotation

a rigid motion where an object turns about an object

For every 90 Degree rotation (Counterclockwise) You…

Switch and then negate the first !

90° Rotation

(-y,x)

180° Rotation

(-x,-y)

270° Rotation

(y,-x)

360° Rotation

(x,y)

Reflection

a rigid motion where an object “Mirrors” or flips about a line

Reflecting over x-axis

(x,-y)

Reflecting over y axis 

(-x,y)

Line y=x

(y,x)

Line y=-x

(-y,-x)

Reflection (Line) Symmetry

When half of the figures matched the other side exactly across a line, creating a mirror image.

Rotation Symmetry

when a figure can be turned onto itself being less than 360°

Magnitude of Symmetry

360°/number of rotations

Congruence Transformations

A series of rigid motions that end up mapping a figure onto another figure.

Reflections in Parallel Lines theorem

If lines K and M are parallel, then Line AA’’ is perpendicular to K and M, and the distance between A and A’’ = 2d, where d is the distance between K and M,.

Reflections in Intersecting lines Theorem

If lines K and M intersect at point P,  the angle of rotation is 2x°, where x° is the measure of the acute or right angle formed by lines K and M.

Similarity Transformatons

a series of rigid motions AND dilations to map one figure onto another.