# Construction

GCSELevel 4-5Cambridge iGCSEEdexcel iGCSE

## Construction

Constructions are accurate drawings/diagrams of lines, angles, and shapes. You will need a pencil, rules, pair of compasses, and a protractor for this topic.

Make sure you are happy with the following topics before continuing:

## Lines

The first construction we will look at is lines. You need to be able to measure and draw lines to the nearest millimeter.

A millimeter is a tenth of a $\text{cm}$ and as they are such a small measurement, it is important to try and be as accurate as possible whilst using a ruler.

You may be asked to draw a line using a ruler.

For example – construct a $79\text{ mm}$ straight line:

Level 4-5GCSECambridge iGCSEEdexcel iGCSE

## Triangles

You may need to construct a triangle, or other $2D$ shape, from the lengths of the sides using a pair of compasses and a ruler.

For example – construct a triangle $ABC$ with the following side lengths:

$AB = 6\text{ cm}\\$ $AC = 3\text{ cm}\\$ $BC = 5\text{ cm}$

Step $\textbf{1}$: To draw line $AB$, measure $6\text{ cm}$ on a ruler and draw a line this length.

Step $\textbf{2}$: To measure line $AC$, set your pair of compasses at $3\text{ cm}$ and draw an arc with $A$ as the center.

Step $\textbf{3}$: To measure line $BC$, set your pair of compasses at $5\text{ cm}$ and draw an arc with $B$ as the center.

Step $\textbf{4}$: Draw a line joining $A$ with the intersection of the $2$ arcs, and repeat for $B$.

Level 4-5GCSECambridge iGCSEEdexcel iGCSE

## Perpendicular Bisector

You may need to construct a perpendicular bisector of a straight line using a pair of compasses and a ruler.

For example, using a pair of compasses and a ruler, find the perpendicular bisector of the line $AB$.

Step $\textbf{1}$: Set your compasses to over half the length $AB$ and place at the point $A$. Draw an arc.

Step $\textbf{2}$: Repeat the same from point $B$, making sure your pair of compasses is set at the same length.

Step $\textbf{3}$: Draw a line passing though the two points where the arcs cross. This is the perpendicular bisector.

Level 4-5GCSECambridge iGCSEEdexcel iGCSE

## Angle Bisector

You may need to construct an angle bisector. This is a line precisely splitting an angle in two.

For example, construct a line, equidistant from line $AB$ and $BC$.

Step $\textbf{1}$: Place the point of your pair off compasses at $B$ and draw a small arc, crossing both $AB$ and $BC$.

Step $\textbf{2}$: Place the point of your pair off compasses where the arc crosses $AB$ and draw an arc between the lines $AB$ and $BC$. Repeat with your compasses at the point the arc crosses $BC$ and draw another arc, keeping your compasses the same length, and making sure the arcs cross over.

Step $\textbf{2}$: Draw a line from $B$ passing through the point the arcs cross. This is the angle bisector.

Level 4-5GCSECambridge iGCSEEdexcel iGCSE

## Construction Example Questions

c is correct as the line starts at the $0$ mark and ends at $9.5\text{ cm}$

d is the correct first step to bisecting an angle.

b is the correct first $2$ steps to drawing the triangle.

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