4To do the exercises in this presentation you will need a ruler, compasses and protractor. We are going to draw some triangles as accurately as possible.You need to be able to draw and measure lines accurate to 1 mm. and angles accurate to 1 degree.
5Can you see a problem with now drawing AC ? Could you draw a triangle ABC with sides AB = 6cm, AC = 4cm and BC = 5cm?Let’s start with AB.AB6cmCan you see a problem with now drawing AC ?Ans: We don’t know what angle AC makes with AB.We have the same problem if we try to draw BC.
6We need C to be in the position that makes BC = 5 cm. Could you draw a triangle ABC with sides AB = 6cm, AC = 4cm and BC = 5cm?Let’s start with AB.AB6cmAC could be here . . .4 cm4cm5cmor here . . .4 cmC4 cmor here . . .CCCarc, radius 4 cm, centred at Aarc, radius 5 cm, centred at BWe need C to be in the position that makes BC = 5 cm.To draw the triangle accurately we always use compasses and draw arcs from A and B.There is only one possible triangle.
7An accurate drawing is often called a construction. Could you draw a triangle ABC with sides AB = 6cm, AC = 4cm and BC = 5cm?AB6cm4cm5cmCAn accurate drawing is often called a construction.We must always show construction lines clearly.
8Tip: We can remember this as SSS ( 3 sides ). There is only one size and shape of triangle we can draw if we are given the lengths of 3 sides.Tip: We can remember this as SSS ( 3 sides ).It doesn’t matter which way up, or which side we start with, all the triangles are congruent.4cm5cm6cm4cm5cm6cm5cm4cm6cm4cm5cm6cm4cm5cm6cm4cm5cm6cm4cm5cm6cm
9If we are given one side of an equilateral triangle we can construct the triangle using compasses and a straight edge instead of a ruler .e.g. Complete the equilateral triangle ABC that has AB as one side.ABCarc, radius AB, centred at Aarc, radius AB, centred at BAns: We can use compasses opened to the length AB and draw arcs at A and B which will meet at C.Decide with your partner how to complete the triangle.Now join AC and BC.
10SUMMARYOnly 1 shape and size of triangle can be drawn if we are given the lengths of 3 sides (SSS).The triangle can be drawn accurately with a ruler and compasses.e.g. Construct a triangle with sides of lengths6 cm, 4 cm and 5 cm.AB6cm4cm5cmarc, radius 4 cm, centred at Aarc, radius 5 cm, centred at BCAn accurate drawing cannot be made without compasses.cont.
11SUMMARYWe can construct an equilateral triangle ABC, if AB is already drawn, using only a straight edge and compasses.ABe.g.arcs of radius AB, centred at A and B.CIf a side of the triangle is not drawn for us, we need a ruler to draw the 1st side.
12All construction lines must be clearly shown. EXERCISEUsing a ruler and compasses only, constructa triangle PQR with sides PQ = 8cm, PR = 6cm and QR = 6cm.Measure angles Q and R.Solution:All construction lines must be clearly shown.8cmPQ6cm6cmQ = 48R = 84R
13All construction lines must be clearly shown. EXERCISE2(a) Using a ruler and compasses only, constructan equilateral triangle with sides of length 7 cm.(b) Measure the angles with a protractor.Solution:All construction lines must be clearly shown.7cmPQ60607cm7cmIf you have been accurate, all the angles will be 60.60R