Year 8 Interactive Maths - Second Edition

## Constructions

Fashion designers, builders, architects and engineers use accurate constructions (or diagrams) to communicate their ideas to others.  In this section, we will consider some of the basic constructions used in geometry.

## Constructing Triangles

If the measurements of three sides, the measurements of two sides and the angle between them, or the measurements of two angles and the side between them are given, then a triangle can be constructed by using a ruler, protractor and compass.

### Constructing a Triangle given Three Sides

#### Example 13

Using a ruler and compass, construct a triangle ABC with AB = 3 cm, BC = 4 cm and AC = 5 cm.

##### Solution:

Step 1:  Draw a line, AB, 3 cm long.
Step 2:  Draw an arc of radius 4 cm with B as the centre.
Step 3:  Draw an arc of radius 5 cm with A as the centre to cut the arc drawn in Step 2 at C.
Step 4:  Join, C, the point of intersection of the two arcs to the points A and B.
Step 5:  Erase the arcs to obtain the required triangle ABC.

## Constructing a Triangle given Two Angles and the Side between them

### Constructing a Triangle given Two Sides and the Angle between them

#### Example 16

##### Solution:

Step 1:  Draw a line, AB, 9 cm long.
Step 2:  Mark an angle of 70º by placing the centre of the protractor at the point A.
Step 3:  Join the 70º mark and the point A. Extend the arm AC until it is 7 cm long.
Step 4:  Join the points B and C to obtain the required triangle ABC.