Practical Geometry

Practical Geometry is about drawing shapes accurately using the instruments in a geometry box: a ruler, a compass, a divider, set squares and a protractor. In this chapter you will draw a circle of a given radius with a compass, draw a line segment of given length using a ruler and compass, and copy a line segment without measuring its length. You will construct a perpendicular to a line through a point on it and through a point not on it, and the perpendicular bisector of a line segment, which divides the segment into two equal parts at right angles. The chapter then turns to angles. You will draw an angle of given measure with a protractor, copy an angle of unknown measure with a compass, and construct the bisector of an angle, the ray that divides it into two equal angles. Finally, using only a ruler and compass, you will construct angles of special measures such as 60 degrees, 30 degrees, 120 degrees, 90 degrees, 45 degrees and 135 degrees.

Detailed Worksheet: Practical Geometry Section A - Definitions (10 marks) 1. Name the instruments in a geometry box and state the use of a compass and a divider. (2 marks) 2. What is the perpendicular bisector of a line segment? (2 marks) 3. What is the bisector of an angle? (2 marks) 4. Define radius and diameter of a circle and state how a compass is set to draw a circle of radius 4 cm. (2 marks) 5. Why is it better to use a compass rather than only a ruler to copy a line segment? (2 marks) Section B - Calculations and Applications (15 marks) 6. Line segment AB is 7.3 cm and CD is 3.4 cm. (i) Construct a segment equal to AB + CD and state its length. (ii) Construct a segment equal to AB - CD and state its length. (iii) Which instruments did you use? (3 marks) 7. An angle of 120 degrees is bisected and then one of the two angles is bisected again. (i) Find the measure of each angle after the first bisection. (ii) Find the measure after the second bisection. (iii) Name the special angles you can construct from 60 degrees by bisecting it once and twice. (3 marks) 8. A line segment PQ of length 9.6 cm is drawn and its perpendicular bisector meets PQ at M. (i) Find PM and MQ. (ii) What is the measure of the angle between PQ and the bisector? (iii) If a point R is on the bisector, compare RP and RQ. (3 marks) 9. Using a protractor, an angle of 75 degrees is drawn. Find (i) the measure of the angle obtained by bisecting it (ii) the measure of its supplement (iii) the measure of the angle formed when a copy of 75 degrees is drawn adjacent to it. (3 marks) 10. A circle has radius 3.5 cm. (i) Find the length of the diameter. (ii) Through the centre, two diameters are drawn perpendicular to each other; name the angle between them. (iii) How many equal parts does this divide the circle into? (3 marks) Section C - Diagrams (10 marks) 11. Draw a line segment AB of length 8.4 cm. Construct its perpendicular bisector using a ruler and compass. Write the steps of construction and verify by measuring that the two parts are equal. (4 marks) 12. Draw an angle of 70 degrees using a protractor and construct its bisector with a ruler and compass. Measure the two parts. (3 marks) 13. Draw a line l and mark a point P not on it. Construct a perpendicular from P to the line l using a ruler and compass. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Explain how to construct an angle of 60 degrees with ruler and compass. Then explain how you would construct angles of 120 degrees and 30 degrees from it. (i) Write the steps. (ii) Why does the arc method produce exactly 60 degrees? (Hint: think of an equilateral triangle.) (iii) Construct 90 degrees and bisect it to get 45 degrees. (5 marks) 15. Rahul draws a circle of radius 5 cm and marks a chord AB. He constructs the perpendicular bisector of AB and finds it passes through the centre. (i) Draw this figure. (ii) Repeat with another chord CD. (iii) What do you notice about the two perpendicular bisectors? (iv) How can this be used to find the centre of a circular plate? (5 marks) 16. Construct an angle of 135 degrees using a ruler and compass. (i) Write the steps, using the fact that 135 = 90 + 45. (ii) Construct the bisector of this angle and state the measure of each part. (iii) Verify using a protractor. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Use a sharp pencil, do not erase construction arcs, and write the steps of construction wherever asked.