Constructions Exercise

1. (a) Using a protractor, construct an angle ABC of 84°. Make AB = 3 cm and BC = 4 cm.
(b) Join A and C to form Δ 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 4 cm, using ruler and compasses.

(b) Bisect each angle, using ruler and compasses only. Mark the intersection of the bisectors with letter O.

3. Using a ruler and compasses only, construct a triangle with sides of length 3.6 cm, 4.9 cm and 7.3 cm. 
Measure the size of each angle with a protractor.

4. Draw a line AB, 5 cm long. Use compasses to construct the perpendicular bisector of the line.

5. a. Construct the triangle shown below using ruler and compasses.

b. Construct the perpendicular bisectors of each side and mark the point where they meet with aC.

6. Draw a line AB, 3 cm long. Construct a line, BC, 4 cm long, at right angles to AB. Join AC and measure its length to the nearest millimetre.

7. Draw a horizontal line XY, 6.7 cm long. Mark a point W, a few centimetres above XY. Construct a line parallel to XY passing through the point W.

8. Construct a kite using ruler and compasses. Make the short sides 3 cm long and the long sides 7 cm long. Draw in the diagonals. Use a protractor to measure the size of the angle between the diagonals.