What does a perpendicular bisector do to a line?

cuts it in half at right angles. Bisect means cut in two; perpendicular means at 90°.

Which tools are used for constructions?

compasses and a ruler. Angles are not measured: they are made with arcs.

What does an angle bisector do?

cuts the angle exactly in half. Every point on it is the same distance from both arms.

Why should construction arcs be left on the drawing?

to show the method used. They earn the method marks.

Every point on the perpendicular bisector of AB is what?

the same distance from A and B. That is what makes it useful for "equidistant" problems.

Constructions · Cambridge IGCSE Mathematics 0580 revision

In plain words

A construction is an accurate drawing made with only a ruler and a pair of compasses, with no protractor. The arcs you draw are the evidence of how you did it, so they must stay on the page.

Three things to know

A triangle from three sides: draw one side, then use the compasses to mark arcs for the other two lengths from each end. Where the arcs cross is the third corner.
Perpendicular bisector of a line: with the compasses set at more than half its length, draw arcs from both ends; join the two points where the arcs cross.
Angle bisector: draw an arc from the corner to cut both arms; from those two points draw arcs that cross; join the corner to the crossing point.

Tips and tricks

Never rub out your construction arcs. No arcs, no marks.
Keep the compasses at the same setting for each pair of arcs.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Constructions: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

What does a perpendicular bisector do to a line?
- copies it
- cuts it in half at right angles (the answer)
- makes it longer
- makes a 45° angle with it
Bisect means cut in two; perpendicular means at 90°.
Which tools are used for constructions?
- a protractor and a ruler
- compasses and a ruler (the answer)
- a calculator
- a set square only
Angles are not measured: they are made with arcs.
What does an angle bisector do?
- doubles the angle
- cuts the angle exactly in half (the answer)
- makes a right angle
- measures the angle
Every point on it is the same distance from both arms.
Why should construction arcs be left on the drawing?
- to make it look neat
- to show the method used (the answer)
- to measure angles
- they should be rubbed out
They earn the method marks.
Every point on the perpendicular bisector of AB is what?
- closer to A
- closer to B
- the same distance from A and B (the answer)
- on the line AB
That is what makes it useful for "equidistant" problems.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

3 questions, 7 marks. Write your answers on paper, then check them.

Constructions

Cambridge IGCSE Mathematics 0580 · 7 marks · papermunch.org

Name ______________________________ Date ______________

Describe how to construct the perpendicular bisector of a line AB.[2]
Show answerHide answer
With the compasses set to more than half of AB, draw arcs above and below the line from A and then from B. Join the two points where the arcs cross.
I got this one
A point lies on the perpendicular bisector of AB. State what is true about its distances from A and from B.[2]
Show answerHide answer
They are equal.
I got this one
Describe how to construct a triangle with sides 7 cm, 5 cm and 4 cm.[3]
Show answerHide answer
Draw a line 7 cm long. Set the compasses to 5 cm and draw an arc from one end; set them to 4 cm and draw an arc from the other end. Join the point where the arcs cross to both ends.
I got this one

Answers: Constructions

1. With the compasses set to more than half of AB, draw arcs above and below the line from A and then from B. Join the two points where the arcs cross.
2. They are equal.
3. Draw a line 7 cm long. Set the compasses to 5 cm and draw an arc from one end; set them to 4 cm and draw an arc from the other end. Join the point where the arcs cross to both ends.