What is the relationship between alternate interior angles in parallel lines?

Alternate interior angles in parallel lines are equal.

When two parallel lines are intersected by a transversal, alternate interior angles are formed on opposite sides of the transversal but inside the parallel lines. These angles are congruent, meaning they have the same measure. This property is a fundamental aspect of parallel lines and is often used in geometric proofs and problem-solving.

To visualise this, imagine two parallel lines, say Line A and Line B, and a third line, the transversal, crossing them. The points where the transversal intersects the parallel lines create four angles at each intersection. The alternate interior angles are the pairs of angles that lie between 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 inside the parallel lines are alternate interior angles.

This property is useful in various geometric problems. For instance, if you know the measure of one alternate interior angle, you can immediately determine the measure of its corresponding angle. This can help in finding unknown angles in more complex geometric figures and in proving that two lines are parallel. Understanding this concept is crucial for solving many types of problems in GCSE Maths, especially those involving parallel lines and transversals.