A triangle from three given sides

Now a triangle that isn't equilateral: sides 4 cm, 5 cm and 6 cm. The compass works here too.

Choose one length as the base, say 4 cm, and call its ends A and B. The third corner is C, with AC = 5 cm and BC = 6 cm.

All the points 5 cm from A lie on a circle with centre A and radius 5 cm. C must be somewhere on it. And C is 6 cm from B, so it is also on a circle with centre B and radius 6 cm. C is where the two circles cross.

You don't need full circles, just arcs:

• Step 1: draw the base AB = 4 cm.
• Step 2: from A, draw a long arc of radius 5 cm.
• Step 3: from B, draw an arc of radius 6 cm to cross it at C.
• Step 4: join AC and BC.

Practise: 4, 4, 6 · 3, 4, 5 · 1, 5, 5 · 4, 6, 8 · 3.5, 3.5, 3.5 cm. Names for two of them: equilateral (all three sides equal) and isosceles (two sides equal).