MOTION IN GEOMETRY: TRANSFORMATIONS 1.6 Geometry

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

TRANSFORMATIONS RIGID TRANSFORMATIONS The movement of a figure in a plane from its original position, the preimage, to a new position, the image. RIGID TRANSFORMATIONS Transformations that do not change the size or shape of a figure.

Transformations Preimage Image The figure before you move it. Usually named with letters Example: A, B, AB… Image The 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 TRANSLATIONS ROTATIONS 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.

ACTIVITY 3, PART 2 The Reflection of a Triangle

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.