Constructions (Edexcel IGCSE Maths)

Spec point — 4.5D

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

  • 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?

• 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?

• 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

Exam Hint

• Make sure you have all the equipment you need for the exam; pen, pencil, ruler, compasses, protractor, calculator

• An eraser and a pencil sharpener can be helpful on these questions as they are all about accuracy

  • But do not erase your construction lines

• Make sure your compasses aren’t loose and wobbly

  • They can usually be tightened with a screwdriver

• Make sure you can see and read the markings on your ruler and protractor