Transformations

Three of the most important transformations are:

Rotation Blue triangle rotating around a center point to show rotation Turn!
Reflection Blue triangle reflected across a vertical axis line to form a pink triangle Flip!
Translation Blue triangle sliding diagonally across a grid to a new position Slide!
Right arrow icon
After any of those transformations (turn, flip or slide), the shape still has the same size, area, angles and line lengths.

Resizing

The other important Transformation is Resizing (also called dilation, contraction, compression, enlargement or even expansion). The shape becomes bigger or smaller:

Resizing Small blue triangle expanding outward to form a larger pink triangle

Congruent or Similar?

If one shape can become another using only a turn, flip and/or slide, the shapes are Congruent.

If a resize is also needed (along with any turns, flips and/or slides), the shapes are Similar.

In other words:

When one shape becomes another ...   The shapes are ...
... using only rotate, reflect and/or translate Right arrow icon

Congruent
... using a resize (may also rotate, reflect and/or translate) Right arrow icon

Similar

Congruent shapes are also similar! They just have a resize scale of 1:1.

Congruent is simply a special case of similar.

Rotation Reflection Translation Isometry Resizing Congruent Similar Symmetry Index Geometry Index