How to Construct an Equilateral Triangle Using a Compass and Straight Edge

Equilateral triangles are those in which the three sides of the triangle have equal lengths. That fact makes this one of the simplest constructions.

Difficulty: Easy

Instructions

Things You'll Need:

• Compass
• Straight edge
• Pen or pencil
• Paper with a segment marked on it showing the desired length of one side

1. If you are not provided with a segment showing the length desired for the side of the triangle, use the straight edge and pencil to draw a segment of a convenient length. Call this segment AB.

2. Anchor the compass on one end of segment AB. We'll call that end A and the other end B.

3. Open the compass so it reaches point B.

4. Draw an arc encompassing about a quarter circle from point B to a point roughly above point A.

5. Anchor the compass on point B.

6. Open the compass until it reaches point A and draw an arc until it intersects the first arc. Call the point of intersection C. This will be the third and final point of the equilateral triangle you're constructing.

7. Draw a straight segment from point A to point C using the straight edge. This segment is AC.

8. Draw a straight segment from point B to point C using the straight edge. This is segment BC. You have now completed an equilateral triangle construction.

Tips & Warnings

• It is fairly easy to prove that in an equilateral triangle the three angles are equal to each other. For any triangle, the sum of the three internal angles is 180 degrees, so each angle in an equilateral triangle is equal to 60 degrees (one third of 180 degrees).
• Make all markings lightly except for segments AB, AC and BC. This will make it easier to see the equilateral triangle once you finish the construction.

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