You know lines and right angles. Two lines in the same flat plane either never meet or cross at exactly one point, and the way they cross gives them names.
Idea clave
Parallel lines never meet, no matter how far they go; they stay the same distance apart ($\overleftrightarrow{AB} \parallel \overleftrightarrow{CD}$). Perpendicular lines cross at a right angle ($\overleftrightarrow{AB} \perp \overleftrightarrow{CD}$). Many crossing lines are neither.
Por qué funciona
Parallel lines point in exactly the same direction. On a dot grid, that means they take the same steps: if one goes 2 over and 1 up, so does the other, so the gap between them never shrinks. Perpendicular lines make four square corners where they cross. On the grid, "2 over, 1 up" is perpendicular to "1 back, 2 up": a quarter turn of the same steps.
Ejemplo resuelto: Use the grid
One line goes 3 over and 1 up. Another goes 3 over and 1 up from a different starting dot. Are they parallel, perpendicular or neither?
- They take the same steps, so they point the same way and never meet.
Respuesta: Parallel
Ejemplo resuelto: In a shape
How many pairs of parallel sides does a rectangle have, and where are its perpendicular sides?
- Top and bottom are parallel; left and right are parallel: 2 pairs.
- Each corner is a right angle, so sides that meet at a corner are perpendicular.
Respuesta: 2 pairs of parallel sides; 4 corners where sides are perpendicular
Error común
Thinking two lines are parallel just because they have not met yet on the page. Lines go on forever; if their directions differ even a little, they cross somewhere. Check their steps on the grid.