Congruent

When one shape can become another using Turns, Flips and/or Slides, then the shapes are Congruent:

Rotation L-shape rotated 90 degrees clockwise on a coordinate grid Turn!
Reflection L-shape reflected across a vertical axis on a coordinate grid Flip!
Translation L-shape slid diagonally up and to the right on a coordinate grid Slide!

After any of those transformations (turn, flip or slide), the shape still has the same size, area, angles and line lengths.

Examples:

Here are 3 examples of shapes that are Congruent:

Two identical blue triangles with one rotated and shifted
Congruent
(Rotated and Moved)
Two identical blue triangles with one reflected horizontally
Congruent
(Reflected and Moved)
Two identical blue triangles with one reflected, rotated, and shifted
Congruent
(Reflected, Rotated and Moved)
Try it yourself: If you take a book and turn it sideways, is it still the same size and shape? Look around you for more examples.

Congruent or Similar?

The shapes need to be the same size to be congruent.

When we need to resize one shape to make it the same as the other, the shapes are Similar.

When we ...   Then the shapes are ...
... only Rotate, Reflect and/or Translate  right arrow

Congruent
... also need to Resize right arrow

Similar

Congruent? Why such a funny word that basically means "equal"? Maybe because they are only "equal" when placed on top of each other. Anyway it comes from Latin congruere, "to agree". So the shapes "agree".

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Similar Congruent Angles Congruent Triangles Transformations Rotation Reflection Translation Isometry Resizing Symmetry Index Symmetry Artist Congruent Angles Geometry Index