AI Tutor
Look at a straight set of train tracks: no matter how far they stretch, the two steel rails never crash into each other, while the wooden cross-ties meet the rails at crisp, square corners.
These two relationships are the backbone of geometry: parallel lines and perpendicular lines.

Lines That Never Meet

Parallel lines are lines on the same flat surface that never intersect, staying the exact same distance apart forever.
In math drawings, we mark parallel lines with matching arrowheads on the lines, and write line AB∥AB \parallel line CDCD using the symbol ∥\parallel.
To verify that lines are truly parallel on a grid, we measure their slope, which is the line's steepness written as riserun\frac{\text{rise}}{\text{run}} (vertical change divided by horizontal change).
If two lines have the exact same slope, they tilt at the same rate and will never cross.
What happens when two lines cross at an exact 90∘90^\circ corner instead?

Square Corners and Right Angles

Perpendicular lines are lines that intersect to form a perfect 90∘90^\circ right angle.
We mark this in figures using a small square symbol in the corner where the lines cross, written as line AB⊥AB \perp line CDCD.