MOTION IN GEOMETRY:

TRANSFORMATIONS

1.6Geometry

CONGRUENCE

• Figures that match exactly (SHAPE & SIZE) are said to be congruent

TRANSFORMATIONS• The movement of a figure in a plane from

its original position, the preimage, to a new position, the image.

• RIGID TRANSFORMATIONSTransformations that do not change the

size or shape of a figure.

Transformations• Preimage

The figure before you move it.

Usually named with letters

Example: A, B, AB…

• ImageThe figure after it has

been moved

Usually named with a letter and a prime symbol (apostrophe)

Example: A’, B’, A’B’…

3 Main Types of Transformations

1. TRANSLATIONS

2. ROTATIONS

3. REFLECTIONS

TRANSLATIONS• Every point of a figure moves in a straight

line, and all points move the same distance and in the same direction.

EXAMPLES

ACTIVITY 1• Translating an image

ROTATIONS• Every point of a figure moves

around a given point known as the center of rotation. All points move the same angle measure.

EXAMPLES

EXAMPLES

ACTIVITY 2• Rotating an image

REFLECTIONS• A line plays the role of a mirror,

and every point in a geometric figure is “flipped” across the line.

EXAMPLES

EXAMPLES

ACTIVITY 3, PART 1• The Reflection of a Point

• If a point is reflected across a line, then the line is the ______________ ____________ of the segment that connects the point with its image.

• The Reflection of a Triangle

ACTIVITY 3, PART 2

• If a triangle is reflected across a line, then the reflected image of the triangle is ____________ to the original triangle

Glide Reflection

Glide Reflection• A combination of a translation and a

reflection.