Definition of Parallel Lines
Grade 7 Geometry โ Understanding lines that never meet
๐ Section 1: Two Possibilities for Lines in a Plane
Imagine you have a flat surface โ like a tabletop or a sheet of paper. This flat surface represents a plane. Now draw two straight lines on it. What can happen?
โ Possibility 1: They Intersect
The two lines share exactly one point. They cross at that point.
These are called intersecting lines.
โ Possibility 2: They Do NOT Intersect
The two lines have no point in common. They never meet, no matter how far you extend them.
These are called non-intersecting (parallel) lines.
โ ๏ธ Key Fact: There are no other possibilities for two lines in a plane. They either intersect at exactly one point, or they don't intersect at all.
Interactive Diagram: Intersecting vs. Non-Intersecting Lines
Drag the points to explore both cases!
Interactive visualization โ available in the full lesson
๐ Section 2: Definition of Parallel Lines
๐ Definition: Two lines in a plane are called parallel if they do not intersect โ that is, they have no point in common.
Notation for Parallel Lines
$a \parallel b$
Read as: "line $a$ is parallel to line $b$"
- Symbol: The symbol $\parallel$ means "is parallel to"
- Visual: Two vertical bars represent two lines that never touch
- Example: If line $m$ is parallel to line $n$, we write $m \parallel n$
๐ก Remember: Parallel lines stay the same distance apart everywhere. They run in the same direction and never converge or diverge.