Constructions (WJEC GCSE Maths & Numeracy (Double Award)): Revision Note

Constructions

What are constructions?

• A construction is a process where you create an accurate geometric object

  • You may have to use a straight edge (ruler), a pair of compasses, and/or a protractor

• 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

  • 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 the perpendicular bisector of a line?

• You can use either

  • a protractor and a ruler,

  • or a pair of compasses and a ruler

• You will receive full marks for using either method in the exam, provided you do it accurately

How do I use a protractor and a ruler to construct a perpendicular bisector?

• STEP 1
  Use the ruler to measure the total length of the line segment that needs to be bisected

• STEP 2
  Calculate half this length, and use it to mark on the midpoint of the line segment

• STEP 3
  Place the protractor with its centre aligned with the marked midpoint, and its base aligned along the line

• STEP 4
  Mark a 90-degree angle above the line segment using the protractor

• STEP 5
  Use the ruler to draw a straight line through the marked midpoint and the 90-degree angle mark

  • This line is the perpendicular bisector

How do I use a pair of compasses and a ruler to construct a perpendicular bisector?

• 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 an angle bisector?

• You can use either

  • a protractor and a ruler,

  • or a pair of compasses and a ruler

• You will receive full marks for using either method in the exam, provided you do it accurately

How do I use a protractor and a ruler to construct an angle bisector?

• STEP 1
  Use your protractor to measure the angle you are going to bisect

  • Make sure the base of the protractor (0°) is along one of the lines forming the angle, and the centre of the protractor is at the vertex (point) of the angle

• STEP 2
  Calculate half of this angle and use your protractor to make a mark at this angle

• STEP 3
  Use your ruler to draw a straight line from the vertex (the point of the angle) to the angle you have marked

  • This line is the angle bisector

How do I use a pair of compasses and a ruler to 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