Alternate-internal angles and corresponding angles

The basic configuration

When a secant line intersects two lines d1 and d2, it forms four angles at each point of intersection, making a total of eight angles. Certain pairs of angles have specific names and useful properties when d1 // d2.

Alternate interior angles

These are two angles situated between the two lines (d1 and d2), but on opposite sides of the secant. If d1 // d2, then the alternate interior angles are equal in measure.

Corresponding angles

These are two angles situated on the same side of the secant, one on line d1 and the other on line d2, in identical positions (for example, both at the top right of their intersection). If d1 // d2, then the corresponding angles are equal.

Summary table

Configuration	Position	If d1 // d2
Alternate-internal	between d1 and d2, on either side of the secant	equal angles
Corresponding	identical position, one on d1, the other on d2	equal angles

Practical example

If an alternate-internal angle measures 62° and the two lines are parallel, then the other alternate-internal angle also measures 62°. It is this property that allows us, for example, to calculate an unknown angle in a triangle or a complex figure without needing a protractor.

Common pitfall

These properties ONLY hold if the lines d1 and d2 are parallel. You must therefore always check or establish that the lines are parallel before using the angle equality; otherwise, the reasoning is incorrect.