Geometrical Shapes

Polygon

A polygon is a plane(2-dimensional) figure that is created by joining a finite number of line segments in the form of a closed loop. In a simple polygon, the sides do not cross each other. Exactly two sides meet at a given vertex.

Simple polygons may be characterized as:

Convex: Any line drawn through the polygon intersects its boundary twice. All its interior angles are less than 180°. All convex polygons are simple.

Concave: Atleast one line can be drawn such that it intersects the the boundary polygon more than two times.  There is at least one interior angle greater than 180°.

Depending upon the number of sides, a polygon may further be called:

• Triangle (3 sided polygon)
• Quadrilateral (4 sided polygon)
• Pentagon (5 sided polygon)
• Hexagon (6 sided polygon)
• Heptagon (7 sided polygon)
• Octagon (8 sided polygon) 

 

For any simple polygon with n sides -

• The sum of internal angles = (n-2) * 180° .
• Sum of internal angles of triangle = 180°
• Sum of internal angles of quadrilateral = 360°
• Sum of internal angles of pentagon = 540° 
• Sum of internal angles of heptagon = 720° 
• The sum of external angles is always 360°

  
A polygon is said to be regular if all its sides and angles are equal.

• A regular quadrilateral is called Square.

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Triangle

Triangle is the shape formed by joining three non-collinear points. (points that do not lie on a line)

Triangles can be classified into the following categories on the basis of angles-

• Acute Angled Triangle: All the 3 internal angles of the triangle are acute .i.e. less than 90°.
• Right Angled Triangle: The triangle has one right angle i.e. angle equal to 90°.
• Obtuse Angled Triangle: One of the internal angles of the triangle is obtuse i.e. more than 90°.

They can also be classified on the basis of sides in the following categories:

• Scalene Triangle: All the the sides of the triangle have unequal lengths.
• Isosceles Triangle: Two of the sides of the triangle have equal length.
• Equilateral Triangle: All the three sides of the triangle have the same length.