Parallel, perpendicular and secant lines

Parallel and Perpendicular Lines

Two lines are parallel if they never intersect, even when extended to infinity. This is denoted as d1 // d2. Two lines are perpendicular if they intersect to form a right angle (90°). We write d1 is perpendicular to d2.

The secant line

When a third line intersects two lines (whether parallel or not), it is called a secant or a transversal. It forms several angles at each point of intersection, which allows us to study interesting relationships between these angles.

Construction properties

• If d1 // d2 and d2 // d3, then d1 // d3 (transitivity of parallelism).
• If d1 // d2 and a line d3 is perpendicular to d1, then d3 is also perpendicular to d2.
• If d1 is perpendicular to d3 and d2 is perpendicular to d3, then d1 // d2.

Practical example

In a squared exercise book, the horizontal lines are all parallel to one another, and the vertical lines are all perpendicular to the horizontal lines. This illustrates these properties well: two vertical lines are therefore parallel to one another, as both are perpendicular to the horizontal lines.

Common pitfall

In a rough sketch, two lines may appear parallel without actually being so. You must always check using the notation in the diagram (identical arrows on parallel lines) or by calculation; never rely solely on a visual assessment.