Lesson 7-1: Angle Relationships and Parallel Lines

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.

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

A transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects two lines, it creates eight angles at the two intersection points.

Examples