Year 9 Interactive Maths - Second Edition

## Geometric Constructions

Many occupations including fashion designers, builders, engineers and architects use accurate constructions (or diagrams) to communicate their ideas to others.  In this part of the chapter we will consider some of the basic constructions used in geometry.

## Constructing Triangles

### Given Two Angles and a Side

#### Example 29

##### Solution:
Step 1 Using a ruler, draw a line interval, AB, 7 cm long.

Step 2

Step 3

ABC
is the required triangle.

### Given Three Sides

#### Example 30

##### Solution:
Step 1 Draw a line interval, AB, 3 cm long.

Step 2

Using a compass, draw an arc with radius 4 cm and with B as the centre.

Step 3

With A as the centre and with radius 5 cm, draw an arc to cut the arc drawn in Step 2 at C.

Step 4

Join AC and BC

ABC is the required triangle.

### Given Two Sides and an Angle

#### Example 31

##### Solution:
Step 1 Draw a line interval, AB, 7 cm long.

Step 2

Step 3

Draw an arc of radius 8 cm with B as the centre to cut AL (extend the arm AL, if needed) at C.

Step 4

Join BC.

ABC is the required triangle.

### Ambiguous Case

Sometimes we can construct more than one triangle with the given measurements.

#### Example 32

##### Solution:
Step 1 Draw a line interval, AB, 7 cm long.

Step 2

Step 3

Step 4