Robinson Tuition
Grade 4 · Foundation and Higher · free GCSE maths worksheet

Constructions with compasses

Perpendicular bisectors, angle bisectors and triangles.

14 original questions, 34 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

A pupil is constructing a 60° angle at point P on a straight line. She puts the compass point on P, sets the radius to 5 cm and draws an arc that crosses the line at Q. She keeps the compasses at 5 cm, puts the point on Q and draws a second arc that crosses the first arc at R.

Explain why angle RPQ is 60°.

2 marks
Show answer
PQ = PR = QR = 5 cm, so triangle PQR is equilateral and each angle is 60 degrees
2

Farida wants to construct a triangle with sides 3 cm, 4 cm and 8 cm using a ruler and compasses.

Explain why she cannot.

2 marks
Show answer
3 + 4 = 7, which is less than 8, so the two shorter sides cannot reach each other
3

Describe, step by step, how to construct a triangle with sides 6 cm, 8 cm and 9 cm using only a ruler and compasses.

3 marks
Show answer
Draw a 9 cm base AB. Arc of radius 6 cm from A. Arc of radius 8 cm from B. Where the arcs cross is C. Join AC and BC.
4

Describe, step by step, how to construct an angle of 60° at a point P on a straight line, using only a ruler and compasses.

3 marks
Show answer
Arc from P crossing the line at Q. Same radius from Q crossing the first arc at R. Join P to R.
5

Draw a line segment AB of length 8 cm.

Using a ruler and compasses only, construct the perpendicular bisector of AB.

You must show all your construction lines.

AB
2 marks
Show answer
Arcs of equal radius (more than 4 cm) drawn from A and from B, crossing above and below AB; the straight line through the two crossing points is the perpendicular bisector, cutting AB at its midpoint at 90 degrees
6

The diagram shows the line AB on a square grid. AB is 7 squares long.

Using a ruler and compasses only, construct triangle ABC with AC = 6 squares and BC = 5 squares. Use the grid to set your compasses. You must show all your construction arcs.

AB
3 marks
Show answer
Triangle ABC with AB = 7 squares, an arc of radius 6 squares from A and an arc of radius 5 squares from B crossing at C, arcs left showing
7

The diagram shows a straight line and a point P on it.

Using a ruler and compasses only, construct an angle of 60° at the point P. Show your construction arcs.

P
3 marks
Show answer
60 degree angle at P with both arcs of equal radius shown
8

Describe how to construct an angle of 30° at a point P on a straight line, using only a ruler and compasses. (Hint: start with a 60° angle.)

3 marks
Show answer
Construct 60 degrees at P, then bisect it using compasses
9

A triangle is constructed with sides 5 cm, 7 cm and 9 cm.

Which angle is the largest? Give a reason.

2 marks
Show answer
The angle opposite the 9 cm side
10

Draw an angle ABC of 70° using a protractor, where B is the vertex of the angle.

Using a ruler and compasses only, construct the bisector of angle ABC.

You must show all your construction lines.

70°ABC
2 marks
Show answer
An arc from B crossing BA and BC, then equal arcs from those two crossing points meeting inside the angle; the line from B through that meeting point bisects the angle into two 35 degree angles
11

Describe how to construct an angle of 45° at a point P on a straight line, using only a ruler and compasses.

3 marks
Show answer
Construct a 90 degree angle at P using the perpendicular at a point method, then bisect it
12

Draw a straight line 10 cm long. Mark a point P about 4 cm above the line.

Using a ruler and compasses only, construct the perpendicular from P to the line.

You must show all your construction lines.

P
2 marks
Show answer
An arc from P crossing the line at two points, then arcs of equal radius from those two points crossing below the line; the line from P through that crossing point is perpendicular to the original line
13

Draw a straight line 10 cm long. Mark a point M on the line, about halfway along.

Using a ruler and compasses only, construct the line perpendicular to the line at the point M.

You must show all your construction lines.

M
2 marks
Show answer
Equal arcs from M crossing the line either side at X and Y, then larger equal arcs from X and Y crossing above the line; the line through M and that crossing point is perpendicular to the original line at M
14

Using a ruler and compasses only, construct an isosceles triangle ABC in which AB = 7 cm and AC = BC = 5 cm.

You must show all your construction arcs.

AB
2 marks
Show answer
Draw AB = 7 cm; arcs of radius 5 cm from A and from B cross at C; joining AC and BC gives the required isosceles triangle

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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