In geometry, an equilateral triangle is a triangle in which all three sides are equal. In traditional or Euclidean geometry, equilateral triangles are also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. They are regular polygons, and can therefore also be referred to as regular triangles.

http://en.wikipedia.org/wiki/Equilateral_triangle

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.

(Our solved example in mathguru.com uses the below concept. This is our own explanation, it is not taken from Wikipedia.)

To construct an equilateral triangle when its altitude is given

E.g.: Construct an equilateral triangle whose altitude is x units

Steps of Construction:

1. Draw any line segment PQ.

2. Take a point D on PQ and At D, construct perpendicular DR to

PQ. From DR, cut off DA = 4 cm.

3. At A, construct ∠DAS = ∠DAT = × 60° = 30° on either side of AD.

Let AS and AT meet PQ at points B and C respectively.

Then, ABC is the required equilateral triangle.