Parallel and Perpendicular Lines

This page focuses on the properties and theorems related to parallel and perpendicular lines. It provides formal statements and proofs for these important geometric concepts.

Definition: Two lines r and s (not parallel to the y-axis) with equations y = mx + q and y = m₁x + q₁ are parallel if and only if they have the same slope: m = m₁.

The page includes a proof for the theorem on parallel lines, emphasizing the importance of the slope in determining the relationship between two lines.

Highlight: The coefficiente angolare retta (slope of a line) plays a crucial role in determining whether lines are parallel or perpendicular.

The document then presents the theorem for perpendicular lines:

Definition: Two lines r and s (not parallel to the axes) with equations y = mx + q and y = m₁x + q₁ are perpendicular if and only if the product of their slopes is equal to -1: m * m₁ = -1.

This theorem provides a clear mathematical condition for perpendicularity, which is essential for solving geometric problems involving intersecting lines.

Example: To determine if two lines are perpendicular, calculate their slopes and check if their product equals -1.

The page concludes with these theorems, providing students with a solid foundation for understanding the relationships between lines in coordinate geometry.