Unit 2: Transformations, Rigid Motions, and Congruence

Properties of Rotations?

1) Transform lines to lines, segments to segments, rays to rays. 2) Preserve distance and length. 3) Preserve angle.

Geometric Fact

A line rotated 180 degrees about a point NOT on the line will always result in another line that is parallel to the original.

How do Rotations work?

A transformation in which a plane figure turns around a fixed center point.

Symmetry of a Figure

A transformation that maps a figure onto itself (also known as carrying a figure onto itself)

Isosceles Triangle

A triangle with at least two sides of equal length.

Vertex Angle

Angle between the congruent sides.

Regular Polygon

Any polygon whose sides have all equal lengths and whose angles all have equal measures.

What is a Dilation?

Bigger/Smaller, Enlarge/Reduce

Base Angles

Either of the angles of a triangle that have one side in common with the base

Alternate Interior Angle Pairs

Either side of the transversal Knees of the "Z"

Congruent

Equal in measure, have same shape and size

What is a Reflection?

Flip

Reflections

It is basically a 'flip' of a shape over the line of reflection.

One rigid motion true ONLY for Translations

Map lines to parallel lines.

Composite Transformations

Multiple rigid motions we combine to produce an image.

Rigid Motions

Preserve Angle Measure

What are 4 basic types of transformations?

Rotation, Reflection, Translation, and Dilation.

Properties of a Figure

Size + Shape or Length/Distance + Angle

What is a Translation?

Slide/Move

What is a Rotation?

Turn

Congruence

Two figures are congruent if a sequence of rigid motions can be found that make the two figures coincide (lie exactly on top of each other).

What is a Transformation?

general term for four specific ways to manipulate the shape of a point, a line, or shape. The original shape of the object is called the pre-image and the final shape and position of the object is the image under the transformation.