What is the property of alternate exterior angles in parallel lines?

Alternate exterior angles in parallel lines are equal.

When two parallel lines are intersected by a transversal, alternate exterior angles are formed on opposite sides of the transversal and outside the parallel lines. These angles are congruent, meaning they have the same measure. This property is a direct consequence of the parallel nature of the lines and the way the transversal intersects them.

To visualise this, imagine two parallel lines, labelled as Line A and Line B, and a transversal line crossing them. The points where the transversal intersects Line A and Line B create four angles at each intersection. The alternate exterior angles are the pairs of angles that lie outside the parallel lines and on opposite sides of the transversal. For example, if the transversal intersects Line A at point P and Line B at point Q, the angles at P and Q that are on opposite sides of the transversal and outside the parallel lines are alternate exterior angles.

This property is useful in various geometric proofs and problems. For instance, if you know one of the alternate exterior angles, you can easily determine the measure of the other. This can help in solving for unknown angles in more complex geometric figures. Understanding this concept also reinforces the idea that parallel lines maintain a consistent relationship with transversals, which is a fundamental aspect of Euclidean geometry.