Constructions (Edexcel GCSE Maths)

Constructions

What are constructions?

• A construction is a process where you create an accurate geometric object using a pair of compasses and a straight edge (and a pencil)

• There are several types of construction you must be able to carry out:

  • A perpendicular bisector of a line

    • This is a line that cuts another one exactly in half (bisects) but also crosses it at a right angle (perpendicular)

    • It shows a path that is equidistant (equal distance) between the two endpoints of the line

  • A perpendicular from a point to a line

    • This is the shortest path between the point and the line

    • It will meet the line at a right angle

  • An angle bisector

    • This is a line that cuts an angle exactly in half (bisects)

    • It shows a path that is equidistant (equal distance) between the two lines that form the angle

How do I construct a perpendicular bisector of a line?

• STEP 1
  Set the distance between the point of the compasses and the pencil to be more than half the length of the line

• STEP 2
  Place the point of the compasses on one end of the line and sketch an arc above and below the line

• STEP 3
  Keeping your compasses set to the same distance, place the point of the compasses on the other end of the line and sketch an arc above and below the line

  • The arcs should intersect each other both above and below the line

• STEP 4
  Connect the points where the arcs intersect with a straight line

How do I construct a perpendicular from a point to a line?

• STEP 1
  Set the distance between the point of your compasses and the pencil to be greater than the distance between the point P and the line

• STEP 2
  Placing the point of the compasses on the point P, draw an arc that intersects the line in two places

• STEP 3
  Set the distance between the point of the compasses and the pencil to be more than half the distance between the two points of intersection on the line

• STEP 4
  Place the point of the compasses on one point of intersection and sketch an arc on the opposite side of the line to P

• STEP 5
  Keeping your compasses set to the same distance, place the point of the compasses on the other point of intersection and sketch an another arc

  • The arcs should intersect

• STEP 6
  Connect the point where the arcs intersect to point P with a straight line

How do I construct an angle bisector?

• STEP 1
  Set the distance between the point of your compasses and the pencil to be about half the distance of the smallest line that makes the angle

  • The precise distance is not important

• STEP 2
  Place the point of the compasses where the lines meet and sketch an arc that intersects both of the lines that form the angle

• STEP 3
  Keeping your compasses set to the same distance, place the point of the compasses on one of the points of intersection and sketch an arc

• STEP 4
  Keeping your compasses set to the same distance, place the point of the compasses on the other point of intersection and sketch an arc

  • This should intersect the last arc you drew

• STEP 5
  Join the point of the angle to the point of intersection with a straight line