What is the defining property of perpendicular lines?

The defining property of perpendicular lines is that they intersect at a right angle. When two lines are perpendicular, the angle formed at their intersection is exactly 90 degrees. This characteristic is fundamental in geometry and is often used to define what we mean by perpendicularity.

While it is true that the slopes of two lines that are perpendicular can be described as opposite and reciprocal, this is a specific mathematical relationship that arises from the concept of perpendicular lines when dealing with their slopes in coordinate geometry. However, when identifying the core defining feature of perpendicular lines, the emphasis should be placed on the nature of their intersection, which is a right angle.

The alternative options do not accurately capture the essence of perpendicular lines. For instance, lines that have equal slopes would be parallel and never intersect. The relationship of slopes being opposite and reciprocal supports the idea mathematically but does not serve as the primary definition of perpendicular lines. Lastly, lines that are parallel do not intersect at any angle and therefore cannot be considered perpendicular. Thus, the clear and defining property of perpendicular lines remains their intersection at a right angle.