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Example:Construct Equilateral Triangle

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Explanation:

Equilateral triangle

 Equilateral triangle An equilateral triangle is a regular polygon. Type triangle, 2-simplex Edges and vertices 3 Schläfli symbol {3} Coxeter-Dynkin diagrams Symmetry group D3 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

(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.