Parallel, perpendicular and intersecting lines

Key notes:

1. Definitions

  • Parallel Lines: Two lines that are always the same distance apart and never meet, no matter how far they are extended. They have the same slope.
  • Perpendicular Lines: Two lines that intersect at a right angle (90 degrees). The slopes of perpendicular lines are negative reciprocals of each other.
  • Intersecting Lines: Two lines that cross each other at any angle. They meet at a point called the point of intersection.

2. Properties

  • Parallel Lines:
    • Symbol: || (e.g., line A || line B)
    • Example: Rails of a train track.
  • Perpendicular Lines:
    • Symbol: ⊥ (e.g., line A ⊥ line B)
    • Form right angles at the point of intersection.
    • Example: The corner of a square or rectangle.
  • Intersecting Lines:
    • Can form various angles.
    • Example: The intersection of two roads.

3. Identifying Lines

  • Use a ruler to draw and identify the types of lines:
    • For parallel lines, ensure they are equidistant.
    • For perpendicular lines, use a protractor to check for a 90-degree angle.
    • For intersecting lines, simply draw two lines that cross.

Learn with an example

📢 Are these lines perpendicular?

  • yes
  • no

Look at this figure:

These lines are not perpendicular. They intersect but do not make square corners.

📢 Are these lines parallel?

  • yes
  • no

Look at this figure:

These lines are not parallel. They intersect at one point.

📢 Are these lines perpendicular?

  • yes
  • no

Look at this figure:

These lines are not perpendicular. They intersect but do not make square corners.

Let’s practice!🖊️