Two polygons with the same shape are called **similar polygons.** The symbol for “is similar to” is ∼. Notice that it is a portion of the “is congruent to” symbol, ≅. When two polygons are similar, these two facts *both* must be true:

- Corresponding angles are equal.

- The ratios of pairs of corresponding sides must all be equal.

In Figure 1*ABCD* ∼ quadrilateral *EFGH.*

**Figure 1 **Similar quadrilaterals.

This means: *m* ∠ *A* = *m* ∠ *E*, *m* ∠ *B* = *m* ∠ *F*, *m* ∠ *C* = *m* ∠ *G*, *m* ∠ *D* = *m* ∠ *H*, and

It is possible for a polygon to have one of the above facts true without having the other fact true. The following two examples show how that is possible.

In Figure 2

**Figure 2** Quadrilaterals that are not similar to one another.

Even though the ratios of corresponding sides are equal, corresponding angles are not equal (90° ≠ 120°, 90° ≠ 60°).

In Figure 3*FGHI* is not similar to quadrilateral *JKLM.*

**Figure 3 ***Quadrilaterals that are not similar to one another.*

Even though corresponding angles are equal, the ratios of each pair of corresponding sides are not equal (3/3≠5/3).

**Example 1:** In Figure 4*ABCD* ∼ quadrilateral *EFGH.* (a) Find *m* ∠ *E.* (b) Find *x.*

**Figure 4 ***Similar quadrilaterals.*

(a) *m* ∠ *E* = 90° (∠ *E* and ∠ *A* are corresponding angles of similar polygons, and corresponding angles of similar polygons are equal.)

(b) 9/6 = 12/ *x* (If two polygons are similar, then the ratios of each pair of corresponding sides are equal.)