Constructing triangles: three sides
The Maths Habit
Ali has three sticks: 3 cm, 4 cm and 9 cm long. Can Ali make a triangle with them?
No. Even laid end to end, 3 + 4 = 7 does not reach across 9.
- Construct
- Draw accurately with a ruler and compasses.
- Vertex
- A corner of a shape.
- Arc
- Part of a circle.
Three sides
- Draw the longest side as the base.
- Open the compasses to the length of the side.Arc from one end of the base.
- Open them to the third side. Arc from the other end.
- Join both ends to where the arcs cross.The corner is this far from A and this far from B.
C is 5 cm from A and 6 cm from B. Where have you found a point like that before?
Last lesson: two arcs, one from each point. C is where they cross.
How wide are the compasses for the arc from A?
Which end does the 6 cm arc come from?
Can these make a triangle?
Construct triangle ABC with AB = 7 cm, AC = 5 cm and BC = 6 cm. Leave your arcs showing. Arcs of 5 cm from A and 6 cm from B
Construct triangle DEF with DE = 8 cm, DF = 6 cm and EF = 4 cm. The arc from D is drawn. Arc of 4 cm from E
Construct triangle ABC with AB = 7 cm, AC = 5 cm and BC = 6 cm. Leave your arcs showing. Arcs of 5 cm from A and 6 cm from B
Construct triangle GHJ with GH = 6 cm, GJ = 5 cm and HJ = 4 cm. The arc from G is drawn. Arc of 4 cm from H
Construct triangle ABC with AB = 7 cm, AC = 5 cm and BC = 6 cm. Leave your arcs showing. Arcs of 5 cm from A and 6 cm from B
Construct triangle PQR with PQ = 8 cm, PR = 4.5 cm and QR = 6 cm. Leave your arcs showing. 4.5 cm from P, 6 cm from Q
Construct triangle ABC with AB = 7 cm, AC = 5 cm and BC = 6 cm. Leave your arcs showing. Arcs of 5 cm from A and 6 cm from B
Construct triangle LMN with LM = 4 cm, LN = 6.5 cm and MN = 3.5 cm. Leave your arcs showing. 6.5 cm from L, 3.5 cm from M
Construct triangle ABC with AB = 7 cm, AC = 5 cm and BC = 6 cm. Leave your arcs showing. Arcs of 5 cm from A and 6 cm from B
Construct triangle STU with ST = 5 cm, SU = 5 cm and TU = 5 cm. Leave your arcs showing. 5 cm from S and from T
Answer sheet
Thumbs up if it is right. Thumbs down if it is wrong.
The compasses for a 5 cm side are opened to 5 cm.
Right3 cm, 4 cm and 6 cm make a triangle.
RightYou can rub out the arcs once the triangle is drawn.
Wrong5 cm, 5 cm and 10 cm make a triangle.
Wrong: it is flat
Construct an angle of 60° without a protractor.
An equilateral triangleTwo sides of a triangle are 5 cm and 9 cm. The third is a whole number of cm. What is the longest it can be?
13 cmConstruct a rhombus with sides of 5 cm and one diagonal of 8 cm.
5, 5, 8 twice
A triangle has sides of 7 cm, 6 cm and 4 cm. The 7 cm side is drawn first. What widths are the compasses set to?
6 cm and 4 cmAB = 4 cm. Construct ABC with AC = 3.5 cm, BC = 3 cm.
Arcs of 3.5 cm and 3 cmCan 3 cm, 4 cm and 8 cm make a triangle? Explain.
No, 3 + 4 is less than 8