MA19.GDA.24

Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

Students know:

Characteristics of translations, rotations, and reflections including the definition of congruence.
Techniques for producing images under transformations using graph paper, tracing paper, compass, or geometry software.
Geometric terminology (e.g., angles, circles, perpendicular lines, parallel lines, and line segments) which describes the series of steps necessary to produce a rotation, reflection, or translation.

Students are able to:

Use geometric descriptions of rigid motions to accurately perform these transformations on objects.
Communicate the results of performing transformations on objects.

Students understand that:

Any distance preserving transformation is a combination of rotations, reflections, and translations.
If a series of translations, rotations, and reflections can be described that transforms one object exactly to a second object, the objects are congruent.

Example: $\Delta ABC$ is congruent to $\Delta XYZ$ since a reflection followed by a translation maps $\Delta ABC$ onto $\Delta XYZ$.