Constructing triangles GM3.2 Core Plenary This triangle is made from these three lines. Find a simple rule which tells you whether or not three lines can be used to make a triangle. How many different triangles can be made from lines of length 1 cm, 2 cm, 3 cm and 4 cm (you can use each line more than once). Jot down what they are – you don’t need to draw them. Sort your list into scalene, equilateral and isosceles triangles. Preamble This activity involves investigating the lengths of sides of triangles Allow pupils time to have a reasonable attempt at finding the rule – the construction shown should give them a hint (they will probably not have explicitly encountered the rule before). Possible content Properties of triangles, informal use of SSS construction. Resources None. Solution/Notes All sides must be less than the sum of the other two. The triangles are: 1-1-1, 2-2-2, 3-3-3, 4-4-4 (equilateral) 1-2-2, 1-3-3, 1-4-4, 2-2-3, 2-4-4, 2-3-3, 3-3-4, 3-4-4 (isosceles) 2-3-4 (scalene)