Explanation:
Equilateral triangle
Equilateral
triangle

An equilateral triangle is a regular
polygon.

Type

triangle,
2simplex

Edges and vertices

3

Schläfli symbol

{3}

CoxeterDynkin diagrams


Symmetry group

D_{3}

Area


Internal angle (degrees)

60°

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.