Constructing an equilateral triangle

Construct an equilateral triangle using a ruler and a compass.

An equilateral triangle has all three sides equal. It is the most balanced triangle. Let's construct one with sides of 4 cm.

With just a ruler, you could: draw AB = 4 cm, then try to mark C so that AC = 4 cm and BC = 4 cm. But there are endless points 4 cm from A, and most aren't 4 cm from B. You'd have to keep moving C and measuring again.

A compass does it at once.

Step 1: draw the base AB = 4 cm.
Step 2: open the compass to 4 cm, put the point on A, and draw a long arc.
Step 3: keep it at 4 cm, put the point on B, and draw an arc crossing the first. Call the crossing C.
Step 4: join AC and BC.

Why does it work? Every point on the arc from A is exactly 4 cm from A (the arc is part of a circle with centre A). Every point on the arc from B is 4 cm from B. C is on both arcs, so it is 4 cm from A and from B. No guessing needed!

An arc from A holds every point at the right distance from A, so where two such arcs cross, both distances are right at once.

Where two arcs cross, both distances are right.

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