Constructing Perpendicular and Parallel lines

Concept sheet | Mathematics
Definitions
  • Two lines are parallel when they do not have a point in common.
  • Two lines are perpendicular when they intersect at right angles.

Parallel and perpendicular lines can be drawn using a set square and a ruler.

Constructing Two Perpendicular Lines

A line that is perpendicular to another can be traced using a set square and a ruler by following these steps:

Rule
  1. Place one side of the set square’s right angle along the first segment with the right angle’s vertex coinciding with one end of the segment.

  2. Keeping the set square in place, draw a line perpendicular to the first segment following the second side of the right angle.

  3. If necessary, move the square along the perpendicular to make it longer.

  1. Place one side of the set square’s right angle along the first segment with the right angle’s vertex coinciding with one end of the segment.

    Équerre

  1. Keeping the set square in place, draw a line perpendicular to the first segment following the second side of the right angle.

Équerre

  1. If necessary, move the square along the perpendicular to make it longer.

Équerre

Constructing Two Parallel Lines

A line parallel to another can be traced using a set square and a ruler by following these steps:

Rule
  1. Place one side of the set square’s right angle along the first segment. Then, place the ruler against the other side of the set square’s right angle.

  2. Slide the set square along the ruler, keeping it in place to keep the direction of the line.

  3. Draw a new straight line parallel to the first without moving the set square.

  1. Place one side of the set square’s right angle along the first segment. Then, place the ruler against the other side of the set square’s right angle.

Square.

  1. Slide the set square along the ruler, keeping it in place to keep the direction of the line.

Square.

  1. Draw a new straight line parallel to the first without moving the set square.

Square.