Geometrical constructions

Use the circle shown below, together with its centre indicated, to demonstrate this.

Feb/March 2017

Segment AB forms one side of equilateral triangle ABC.

Feb/March 2017

Complete parts (a)(i) and (b)(i) of this question with a straight edge and compasses only. Include every construction arc.

Feb/March 2017

For this question, use only a straight edge and compasses, and draw every construction arc.

Feb/March 2018

For this question, use only a straight edge and compasses, and show every construction arc.

Feb/March 2018

Construct the equilateral triangle $ABC$.

Feb/March 2019

A straight line segment is shown with its ends labelled A and B.

Feb/March 2020

Draw a straight line joining point S to point T.

Feb/March 2024

Using only a ruler and compasses, construct triangle $DEF$. Keep the construction arcs on your drawing.

Feb/March 2024

Use a ruler and compasses for this question. The rectangle $ABCD$ is shown.

May/June 2015

Draw a triangle with side lengths 5 cm, 6 cm and 7 cm.

May/June 2015

The diagram indicates the positions of the three points, $A$, $B$ and $C$.

May/June 2015

For triangle $ABC$, the length of $AC$ is $10\text{ cm}$ and the length of $BC$ is $9\text{ cm}$.

May/June 2015

Using only a straight edge and compasses, construct the bisector of angle $ABC$.

May/June 2016

The diagram depicts triangle $ABC$ with the vertices marked $A$, $B$ and $C$.

May/June 2016

The diagram illustrates a rectangular garden split into several sections. $FG$ acts as the perpendicular bisector of $BC$. The arc $HJ$ is centred at $D$ and has a radius of 20 m. $CE$ is the bisector of angle $DCB$. Diagram NOT TO SCALE.

May/June 2016

The figure shows triangle $ABC$.

May/June 2016

On the page, draw straight line $AB$, with $A$ placed on the left and $B$ on the right.

May/June 2016

The scale drawing depicts a park, $ABCDE$. The scale is 1 centimetre represents 20 metres. North is indicated.

May/June 2016

The diagram displays the locations of points $A$, $B$ and $C$.

May/June 2017

Triangle $ABC$ is displayed, with points $A$, $B$ and $C$ labelled.

May/June 2017

With ruler and compasses only, construct triangle $ABC$. Include all of your construction arcs.

May/June 2017

ABCD is a quadrilateral. The diagram displays vertices A, B, C, and D joined consecutively to make a quadrilateral.

May/June 2018

Use only a straight edge and compasses to construct the locus of all points equidistant from A and B. In the diagram, point A is shown on the left and point B on the right.

May/June 2018

The scale diagram shows three sides of a wildlife park, namely AB, BC and CD. According to the scale, 1 centimetre stands for 50 metres.

May/June 2018

Triangle $ABC$ is illustrated.

May/June 2019

Shown is a pyramid with a square base. Its triangular side faces are congruent isosceles triangles. The base edge measures $4\text{ cm}$ and a sloping edge measures $6\text{ cm}$. The diagram is not drawn to scale.

May/June 2019

In the scale drawing of rectangle ABCD, 1 centimetre corresponds to 20 metres.

May/June 2019

A rhombus with side length $6.5\text{ cm}$ can be formed by constructing two triangles.

May/June 2021

From point P, draw a line that is perpendicular to this line.

May/June 2021

A rhombus has a side length of $6.5$ cm. It may be formed by drawing two triangles. One diagonal of the rhombus has already been drawn.

May/June 2021

A straight line with the label L is drawn.

May/June 2022

A straight line AB is drawn, with A at one end and B at the opposite end.

May/June 2022

The diagram depicts a line segment with endpoints marked A and B.

May/June 2023

The diagram contains two straight lines, AB and AC, which meet at A; B is placed to the right of A and C is positioned above A. The angle at A between AB and AC is labelled x.

May/June 2024

The diagram contains line AB and point P.

May/June 2025

In triangle $ABC$, $AC = 6.4\text{ cm}$ and $BC = 5.3\text{ cm}$. With a ruler and compasses only, construct triangle $ABC$. Keep your construction arcs visible. The line $AB$ has already been drawn for you.

May/June 2025

For triangle $ABC$, the lengths $AC = 21\text{ m}$ and $BC = 15.9\text{ m}$ are given. With only a ruler and compasses, finish the scale drawing of the triangle. Take the scale as $1\text{ cm}$ representing $3\text{ m}$. The side $AB$ has already been drawn.

May/June 2025

A side measuring $85$ mm has already been drawn for you.

Oct/Nov 2015

For this question, use only a ruler and compasses, and make sure that every construction arc is shown. On a scale where 1 centimetre represents 50 metres, construct a triangle whose sides are 550 m, 450 m and 300 m. The 300 m side has already been drawn.

Oct/Nov 2015

Construct the perpendicular bisector of $AB$.

Oct/Nov 2015

The diagram depicts a triangle whose vertices are labelled $A$, $B$ and $C$.

Oct/Nov 2016

For triangle $ABC$, the lengths are $AB = 7\text{ cm}$, $BC = 4\text{ cm}$ and $AC = 6\text{ cm}$. With only a ruler and compasses, construct triangle $ABC$. The side $BC$ has already been provided. The diagram shows a vertical line with $B$ at the top and $C$ at the bottom.

Oct/Nov 2016

Construct the locus of points that lie inside the triangle and are $5$ cm from $B$.

Oct/Nov 2016

The diagram depicts angle $BAC$, with $A$ as the vertex and $B$ and $C$ placed on two rays starting from $A$.

Oct/Nov 2016

The diagram gives the positions of three towns, $A$, $B$ and $C$. $B$ lies 24 km due North of $A$. $C$ is 18 km from $A$ and 15 km from $B$.

Oct/Nov 2016

The figure depicts rectangle $ABCD$.

Oct/Nov 2017

$AB$ lies on a straight line. The diagram shows a horizontal line segment with point $A$ at the left-hand end and point $B$ at the right-hand end.

Oct/Nov 2017

A park $ABCD$ is shown in the scale drawing. The scale means 1 centimetre stands for 20 metres. A North arrow is included, and the points are marked $A, B, C, D$.

Oct/Nov 2017

The diagram is a scale drawing of Tariq’s garden. The scale is 1 centimetre represents 2 metres. It shows two points labelled Tree and one point labelled Bird bath.

Oct/Nov 2017

On the diagram, BL bisects angle ABC, while MN is the perpendicular bisector of AB.

Oct/Nov 2017

The diagram displays pentagon $ABCDE$.

Oct/Nov 2018

The diagram displays triangle ABC and an arc centred at C with radius 6.5 cm.

Oct/Nov 2018

The figure depicts a pentagon $ABCDE$.

Oct/Nov 2018

Find the probability that the bulb he picks is white.

Oct/Nov 2018

The diagram shows the triangle’s base. The other two sides are 6 cm and 4 cm long.

Oct/Nov 2019

The diagram is a scale drawing of Lei’s garden, $PQRS$. The scale is 1 centimetre represents 2 metres.

Oct/Nov 2019

The scale diagram represents triangle $ABC$. The scale is 1 centimetre represents 8 kilometres.

Oct/Nov 2019

The diagram presents a scale drawing of Lei’s garden, $PQRS$. The scale is 1 centimetre to 2 metres.

Oct/Nov 2019

Draw triangle $ABC$ using only a ruler and compasses.

Oct/Nov 2019

In triangle $ABC$, $BC = 7.6\text{ cm}$ and $AC = 6.2\text{ cm}$. With a ruler and compasses only, construct triangle $ABC$. Keep your construction arcs visible. Side $AB$ has already been drawn for you.

Oct/Nov 2020

A triangle-shaped field, $ABC$, is given. $AC = 500\text{ m}$ and $BC = 650\text{ m}$. With only a ruler and compasses, finish the scale drawing of field $ABC$. Keep the construction arcs visible. Work to a scale where 1 cm represents 100 m. The side $AB$ has already been drawn. Diagram text: A straight line joins the points marked $A$ and $B$. The label says: "Scale: 1 cm to 100 m".

Oct/Nov 2020

In triangle $ABC$, the lengths $BC = 7.6\,\text{cm}$ and $AC = 6.2\,\text{cm}$ are given. With only a ruler and compasses, construct triangle $ABC$. Keep the construction arcs visible. The side $AB$ has already been drawn. The diagram is a straight line with $A$ marked at the left end and $B$ marked at the right end.

Oct/Nov 2020

Construct a triangle $ABC$.

Oct/Nov 2021

Determine the length of this line in millimetres.

Oct/Nov 2022

In triangle $PQR$, $PR = 5\text{ cm}$ and $QR = 4\text{ cm}$. With only a ruler and compasses, construct triangle $PQR$. Keep the construction arcs visible. The side $PQ$ has already been drawn for you.

Oct/Nov 2022

For triangle $LMN$, the lengths are $LN = 7.5\text{ cm}$ and $MN = 8\text{ cm}$. The side $LM$ is already drawn.

Oct/Nov 2023

With ruler and compasses only, construct triangle $RST$. Keep the construction arcs on your drawing.

Oct/Nov 2023

Triangle $ABC$ has side lengths $AC = 4.2\text{ cm}$ and $BC = 5.6\text{ cm}$. With a ruler and compasses only, construct triangle $ABC$. Keep the construction arcs visible. The side $AB$ has already been drawn for you.

Oct/Nov 2024

In triangle ABC, AB = 8 cm and BC = 6.4 cm. With only a ruler and compasses, construct triangle ABC. Keep the construction arcs visible. AC has already been drawn.

Oct/Nov 2025

Measure the distance of line AB in centimetres.

Oct/Nov 2025

State the length of line AB in centimetres.

Oct/Nov 2025

Using a ruler and compasses only, construct triangle ABC.

Oct/Nov 2025