To 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.
Can you see a problem with now drawing AC ? Ans: We dont know what angle AC makes with AB. Lets start with AB. A B 6 cm Could you draw a triangle ABC with sides AB = 6 cm, AC = 4 cm and BC = 5 cm? We have the same problem if we try to draw BC.
Could you draw a triangle ABC with sides AB = 6 cm, AC = 4 cm and BC = 5 cm? Lets start with AB. A B AC could be here... or here... We need C to be in the position that makes BC = 5 cm. C C C C To draw the triangle accurately we always use compasses and draw arcs from A and B. 6 cm 4 cm 5 cm 4 cm arc, radius 4 cm, centred at A arc, radius 5 cm, centred at B There is only one possible triangle.
Could you draw a triangle ABC with sides AB = 6 cm, AC = 4 cm and BC = 5 cm? A B C 6 cm 5 cm We must always show construction lines clearly. 4 cm An accurate drawing is often called a construction.
5cm 4cm 6cm There is only one size and shape of triangle we can draw if we are given the lengths of 3 sides. It doesnt matter which way up, or which side we start with, all the triangles are congruent. 4cm 5cm 6cm 4cm 5cm 6cm 4cm 5cm 6cm 4cm 5cm 6cm Tip: We can remember this as SSS ( 3 sides ). 4cm 5cm 6cm 4cm 5cm 6cm
A B Decide with your partner how to complete the triangle. Ans:We can use compasses opened to the length AB and draw arcs at A and B which will meet at C. If 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. C Now join AC and BC. arc, radius AB, centred at A arc, radius AB, centred at B
e.g.Construct a triangle with sides of lengths 6 cm, 4 cm and 5 cm. SUMMARY The triangle can be drawn accurately with a ruler and compasses. An accurate drawing cannot be made without compasses. A B 6 cm 4 cm 5 cm C arc, radius 4 cm, centred at A arc, radius 5 cm, centred at B Only 1 shape and size of triangle can be drawn if we are given the lengths of 3 sides (SSS). cont.
A B e.g. We can construct an equilateral triangle ABC, if AB is already drawn, using only a straight edge and compasses. If a side of the triangle is not drawn for us, we need a ruler to draw the 1 st side. SUMMARY C arcs of radius AB, centred at A and B.
EXERCISE 1.Using a ruler and compasses only, construct a triangle PQR with sides PQ = 8 cm, PR = 6 cm and QR = 6 cm. Measure angles Q and R. P Q R 8cm 6cm Q = 48 R = 84 Solution: All construction lines must be clearly shown.
EXERCISE 2(a)Using a ruler and compasses only, construct an equilateral triangle with sides of length 7 cm. (b)Measure the angles with a protractor. P Q R 7cm Solution: 60 If you have been accurate, all the angles will be 60. All construction lines must be clearly shown.