Construction

GCSELevel 4-5Cambridge iGCSEEdexcel iGCSE

Construction Revision

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:

Scale Drawings

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:

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 $B$ .

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.

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.