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 , quadrilateral 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 , quadrilateral QRST is not similar to quadrilateral WXYZ.

Figure 2 Quadrilaterals that are not similar to one another.

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

Figure 3 Quadrilaterals that are not similar to one another.

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

Figure 4 Similar quadrilaterals.

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