Lesson 7: Lines, Angles and Planes

New Concept

This lesson introduces the foundational building blocks of geometry: points, lines, planes, and angles, which are essential for studying shapes and space.

What’s next

This is just the foundation. Next, you'll apply these definitions in worked examples, learning to classify angles and analyze relationships between lines and planes.

Property

A line contains an infinite number of points extending in opposite directions without end. A line has one dimension, length. We use the notation $\overleftrightarrow{AB}$ to name a line.

Examples

• A line passing through points C and D is named $\overleftrightarrow{CD}$ or $\overleftrightarrow{DC}$.
• A ray is different; it's a part of a line with one start point, like a laser beam: $\overrightarrow{CD}$.
• A segment is just a piece with two endpoints, like one side of a ruler: $\overline{CD}$.

Explanation

Picture a perfectly straight road that stretches to infinity in both directions. It's so thin it only has length, no width. You can name this endless road by picking any two points on it!

Property

If two lines in a plane do not intersect, they remain the same distance apart and are called parallel lines. We use the symbol $\parallel$ to show this, like $\overleftrightarrow{QR} \parallel \overleftrightarrow{ST}$.

Examples

• The opposite sides of a rectangle are parallel. For a rectangle ABCD, we can write $\overleftrightarrow{AB} \parallel \overleftrightarrow{DC}$.
• The lines on a sheet of notebook paper are all parallel to each other.
• The top and bottom edges of a whiteboard are parallel.

Explanation

Think of railroad tracks! They run side-by-side forever but never, ever crash. They always stay the same distance apart, creating a perfect, non-intersecting pair. It's like they're partners in not meeting.

Property

Lines that intersect and form 'square corners' are perpendicular lines. We use the symbol $\perp$ to show this, like $\overleftrightarrow{MN} \perp \overleftrightarrow{PQ}$.

Examples

• The intersection of a vertical wall and a horizontal floor creates perpendicular lines.
• In a window frame, the horizontal and vertical pieces are perpendicular: $\overline{EF} \perp \overline{FG}$.
• On a graph, the x-axis and y-axis are perpendicular to each other.

Explanation

When two lines cross to make a perfect 'plus' sign or a square corner, they're perpendicular! It's the most organized way for lines to meet, forming flawless right angles where they intersect.