Drawing Triangles, Squares and Rectangles

1Your drawing tools

• A ruler draws straight lines and measures lengths.
• A protractor measures and draws angles.
• A pair of compasses draws circles and arcs, and copies equal lengths.
• A sharp pencil: a thick line can hide a whole degree.

2Using a protractor

1. Make the arms of the angle long enough to reach the scale. Extend them with your ruler if needed.
2. Put the centre point of the protractor exactly on the vertex of the angle, and its base line exactly along one arm. Hold it still with one finger.
3. A protractor has two scales, one going each way. Use the scale that starts at 0 on the arm under the base line, and read where the other arm crosses it.

To draw an angle, draw one arm first. Put the centre point on its end, find the angle on the scale that starts at 0, mark a small dot, then join the dot to the vertex with your ruler.

Worked example 1: two sides and the angle between them

Draw triangle ABC with AB = 6 cm, angle A = 50° and AC = 4 cm.

1. Draw AB 6 cm long.
2. At A, measure 50° from AB and draw a line.
3. Measure 4 cm along that line from A and mark C.
4. Join C to B. The triangle is finished.

Worked example 2: one side and two angles

Draw triangle ABC with AB = 7 cm, angle A = 40° and angle B = 60°.

1. Draw AB 7 cm long.
2. At A, measure 40° and draw a long line.
3. At B, measure 60° on the same side of AB and draw a long line.
4. The two lines cross at C.
5. Check: angle C should be 180° − 40° − 60° = 80°. Measure it. If it is not 80°, one of your angles is wrong.

Worked example 3: a square with sides of 5 cm

1. Draw AB 5 cm long.
2. At A and at B, measure 90° and draw lines going up.
3. Measure 5 cm up each line and mark D (above A) and C (above B).
4. Join D to C.
5. Check: DC should be 5 cm, and the two diagonals AC and BD should be equal (about 7.1 cm each).

A rectangle is drawn the same way: for a 6 cm by 4 cm rectangle, draw the 6 cm side, make right angles at both ends, and mark 4 cm up each line.

3Scale drawings

A garden is too big to draw full size, so we use a scale. A scale of 1 : 100 means 1 cm on the drawing stands for 100 cm (1 m) in real life.

Try it yourself

1. A triangle has angles of 65° at A and 45° at B. What will angle C be?
2. You draw a square with sides of 6 cm. What angle do you draw at each corner, and how long is each side?
3. A classroom is 9 m long. How long is it on a plan drawn at 1 : 100?
4. A plan drawn at 1 : 50 shows a table 3 cm long. How long is the real table?

Answers

1. 180° − 65° − 45° = 70°.
2. 90° at every corner, and every side is 6 cm.
3. 900 cm ÷ 100 = 9 cm.
4. 3 × 50 = 150 cm, which is 1.5 m.