## Constructions Exercise

1. (a) Using a protractor, construct an angle ABC of 54°.

Make AB = 4 cm and BC = 5 cm.

(b) Join A and C to form ABC.

(c) Measure the length of AC to the nearest millimetre.

(d) Construct, using ruler and compasses only, the angle bisector of ABC and extend it to meet AC at point D.

2. (a) Construct an equilateral triangle of length 5 cm, using ruler and protractor.

(b) Bisect each angle, using ruler and compasses only.

3. Using a ruler and compasses only, construct a triangle with sides of length 5.6 cm, 4.2 cm and 8.3 cm.

4. On a map drawn using a scale of 1 cm : 5 km, what distance is represented by:

(a) 3 cm? (b) 20 cm? (c) 1.5 cm?

5. A map is drawn using a scale of 1 cm : 5 km. What would be the distance on the map if the real distance between the two places was:

(a) 10 km? (b) 35 km ? (c) 2.5 km?

6. The map below shows two small radio stations. Radios 8ZB and 5ZA.  The map is drawn to scale and 1 cm represents 10 km.

(a) What is the distance between the radio stations?

The broadcasting range of each station is 15 km.

(b) On the diagram, sketch and shade:

(i) The region where 8ZB can be received.

(ii) The region where 5ZA can be received.

(c) Line AB represents the top of a hill. Anywhere within 10 km of the hill

7. Two trampers walk 8 km on a bearing of 80°, then go 10 km on a bearing of 170°.

Draw a scale diagram using 1 cm : 2 km to show their route.

(a) How far, in a straight line, are the trampers from their starting point?

(b) What bearing should the trampers take to go back to the starting point? 8. Construct, using ruler and compasses only, a triangle with two sides of length 2.5 cm and 3.6 cm, and the angle between them equal to a right angle.

9. Using a scale of 1 cm : 5 m, draw a plan of a room 20 m by 30 m. How far is it between opposite corners of the room, to the nearest metre?