Parallel and Perpendicular Lines
Parallel and Perpendicular Lines

Two lines are parallel if one can be translated, without rotation, to lie on top of the other. Two lines are perpendicular if they meet at a right angle (an angle of 90°).
Mathematically, the determination of whether two lines are parallel to each other, perpendicular to each other, or neither is based on their slopes.
Consider two lines, ${L}_{1}$ and ${L}_{2}$, in a plane, with slopes ${m}_{1}$ and ${m}_{2}$, respectively.
The lines ${L}_{1}$ and ${L}_{2}$ are parallel if they have the same slope: ${m}_{1}\={m}_{2}$.
The lines ${L}_{1}$ and ${L}_{2}$ are perpendicular if their slopes are negative reciprocals of each other: ${m}_{1}\=\frac{1}{{m}_{2}}$.




Relationship between Parallel and Perpendicular Lines


Click and drag on the plot below to change the angles between the lines. Rotate the red or blue line about its intersection with the green line and view the corresponding interior angles $\angle \mathrm{\α}$ and $\angle \mathrm{\β}$.
What happens when the angles add up to 90°? to 180°?

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