### Alternate angles

In each diagram below, the two marked angles are called **alternate angles** because they are on alternate sides of the transversal *EF*. The two angles must be between the two lines.

### Alternate angles and parallel lines

When the lines *AB* and *CD* are parallel (as in the diagram below), the alternate angles \(\angle\)*BHF* and \(\angle\)*CGE* are equal.

This can be proven using the previous result that showed that corresponding angles are equal.

\(\angle\)*BHF* = \(\angle\)*DGF* (corresponding *AB *|| *CD*)

\(\angle\)*DGF* = \(\angle\)*CGE* (vertically opposite angles at *G*)

Hence \(\angle\)*BHF *=\(\angle\)*CGE.*

#### Example 2

Find θ in the diagram.

#### Solution

θ = 96° (alternate angles *AB* || *CD)*