## Construction of Triangles and Circles

### Types of Diagrams

 A sketch is a rough diagram which does not have to be too accurate. A drawing is more accurate and can be drawn using a ruler and a protractor for measuring lengths and angles. A construction in mathematics is an accurate drawing done usually using only instruments such as a ruler as a straight edge and a pair of compasses.  When drawing a construction, leave all of your construction arcs and lines. . ### Construction of Triangles and Circles

Triangles are three-sided polygons. Types of triangles include isosceles, scalene and equilateral.

To make a construction certain information is needed about the size of the angles and sides of the shape.

The instruments used for constructions, which include ruler, compasses and protractors are described in What is Geometry?, Topic 29.

Some of the types of constructions with circles and triangles are described below:

 Draw a circle of radius 2 cm Step 1: Extend compasses to 2 cm, using ruler. Step 2: Draw the circle. Construct a triangle ABC with sides of lengths 2 cm, 3 cm and 4 cm. Step 1 Draw side AB, say 4 cm long, with ruler. Step 2 Draw an arc, centre B, radius 3 cm. Step 3 Draw an arc, centre A, radius 2 cm. Step 4 Let the arcs intersect at a point C and thenjoin A and B to C. Draw a triangle PQR with sides PQ = 5 cm RQ = 3 cm and PQR = 57° Step 1 Draw a line PQ of length 5 cm. Step 2 Draw an angle of 57° at Q, using a protractor. Step 3 Draw an arc of 3 cm, centre Q and label it R. Step 4 Join R and P to form triangle PQR. Draw a triangle XYZ with angle Y = 45°angle X= 75° and side XY = 6 cm Step 1 Draw the line XY of length 6 cm. Step 2 Draw an angle of 45° at Y using a protractor. Step 3 Draw an angle of 75° at X. Z is the point where the lines intersect. 