The word *similar* is used in geometry to describe two figures that have identical shapes but are not necessarily the same size. A working definition of similarity can be obtained in terms of angles and ratios of distances.

Two polygons are ** similar** if corresponding angles are congruent and the ratios of corresponding sides are equal.

**Notation.** We use the symbol ~ to denote similarity. Thus, we write

to denote that the polygons *ABCDE* and *QRSTU* are similar. As with congruency, the order of the letters is important.

To say that Δ*ABC* ~ Δ*DEF* means that

and

where *k* is a positive real number.

The constant *k* is called the ** proportionality constant** or the

Note that congruent figures are necessarily similar, but similar figures do not need to be congruent.

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