Ideas in Geometry/Instructive examples/Section 1.1

Consider segment AB with length x.

In order to make an equilateral triangle, we need all side length to be the same and all angle measures to be the same. From segment AB, you would draw a point C such that C is the same distance away from A and B as A is from B, length x. From here you would draw in segment AC and segment BC. Interior angles should all be equal since each of the side length constructed can only lend itself to equal angles, meaning that there is no other way to construct this triangle without equal angles. Thus you can make an equilateral triangle from one segment, with that segment ( such as AB) as its side.

(Hbrozowski 06:14, 25 October 2010 (UTC))