A triangle has three side lengths: 6 cm along the bottom, 4 cm up one side and 5 cm up the other. If two of you were each handed those same three lengths and told to build the triangle, would you both end up with the exact same shape, or could you build different-looking triangles? Hands up: what is your gut feeling?

Watch the board build each triangle from three given sides. The circle tool swings an arc at a set distance, just like your compass: draw the base, swing an arc from each end, and the crossing point is the third corner. Watch where the arcs cross, and watch what happens when they can't.

Today we build triangles from three given sides together on the board. We will work through three sets in turn: first 5 cm, 4 cm and 3 cm; then 6 cm, 6 cm and 4 cm; then 5 cm, 5 cm and 5 cm. Each time a pupil swings the two compass arcs from each end of the base and joins where they cross, and we check together that the triangle closes from exactly those three sides.

We'll build four triangles together on the interactive, one at a time, each a bit harder than the last. Take turns at the board: set the base, swing both arcs, join where they cross. Check the sides match before we move on.

Key Takeaways

• To construct an SSS triangle: draw the base, swing an arc from each end set to the other two sides, and join where they cross.
• The right three side lengths fix one unique triangle — everyone who measures carefully gets the same shape.
• Some side lengths cannot form a triangle: the two shorter sides must add up to more than the longest side, or the arcs never meet.