Teaching Models

Congruence, Symmetry, and Transformations

Two figures are congruent if they can be superimposed so that they fit exactly. It can be shown that two plane polygons are congruent if and only if a one-to-one correspondence can be established between them such that corresponding sides have the same length and corresponding angles have the same measure.

Thus, figures that are the same size and shape are congruent. Corresponding parts of congruent figures are congruent. Congruent figures, such as those below, may be in different positions.

Congruent shapes

A figure has line symmetry if it can be folded in half and the two halves are congruent. The line made by the fold is the line of symmetry. Line symmetry is also called bilateral symmetry. Figures can have no lines of symmetry or an unlimited number of lines of symmetry.

symmetrical shape
symmetrical shape
symmetrical shape
symmetrical shape
No lines of symmetry
1 line of symmetry
3 lines of symmetry
Unlimited lines of symmetry

Teaching Model 16.5: Visual Thinking

Houghton Mifflin Math Grade 3