Transformations
Lessons in this chapter
About Transformations
Transformations covers every rigid and non-rigid move a figure can undergo, and what those moves mean for congruence and similarity.
Translations, Reflections, and Rotations each move a figure without changing its size or shape, and Congruence and Transformations ties them together: two figures are congruent exactly when one maps onto the other using only these size-preserving moves.
Dilations introduces the one transformation that changes size, scaling a figure from a center point by a scale factor, and Similarity and Transformations shows that two figures are similar exactly when a dilation combined with the size-preserving moves maps one onto the other.
All six lessons in this chapter open as Geometry worksheets in the page, including Rotations, Congruence and Transformations and Similarity and Transformations. Each question is scored as you answer it, so a rotation taken clockwise when the problem asked for counterclockwise shows up straight away. The worksheets are free to try, with no login needed for your first 3.
Frequently asked questions
Translations, Reflections and Rotations cover the three rigid motions, each moving a figure without changing its size or shape. Congruence and Transformations then defines two figures as congruent precisely when one can be mapped onto the other by those motions, which is the modern definition the rest of the course uses. Dilations scales a figure about a center point, and Similarity and Transformations defines similarity the same way, as a dilation followed by rigid motions. The chapter sits in the high school Geometry conceptual category (G).
A rigid transformation (translation, reflection, or rotation) preserves a figure's size and shape exactly: only its position or orientation changes.
Two figures are congruent exactly when a sequence of rigid transformations maps one exactly onto the other.
A dilation resizes a figure from a center point by a scale factor, changing its size (though not its shape): unlike rigid transformations, which never change size at all.
Two figures are similar exactly when a dilation, combined with any rigid transformations, maps one onto the other: same shape, not necessarily the same size.
Identify each individual move (which direction and distance for a translation, which line for a reflection, which point and angle for a rotation, or center and factor for a dilation) in the order they’re applied.