Types Of Polygons - Technical Graphics - Weebly

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Basic Constructions
- Bisecting a Line
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- Bisecting an angle
- Constructing a 90° angle
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Triangles
- Parts of a Triangle
- Types of traingle
- Proving a Triangle has 180°
- Incentre of a Triangle
- Orthocentre of a Triangle
- Circumcentre Of a Triangle
- Centroid of a Triangle
- Medians of a Triangle
- Questions >
  - Construct an Equilateral Triangle given one side
  - Construct an isosceles Triangle given the base and altitude
  - Construct an Isosceles Triangle given the leg and apex angle
  - Construct a Triangle 30°, 60°, 90° given the hypotenuse
  - Construct a Triangle given three sides
  - Construct a Triangle given the base angles and the base length
  - Construct a Triangle give two sides and an angle
- Perimeter/Ratio >
  - Construct a Equilateral Triangle with a given a perimeter
  - Construct a Triangle with a given a perimeter in the ratio 2:3:4
Circles
- Parts of a Circle
- Concentric/Eccentric Circles
- Proofs >
  - Prove that the angle in the same segment of a circle is equal
  - Calculate the angle at the centre of a circle
- Questions >
  - Construct a circle given 3 points
- Tangents >
  - Tangent to a point on the circle
  - Tangent to a point outside a circle
  - Construct an exterior tangent to the given circles
  - Construct an Interior tangent to the given circles
Quadrilaterals
- Types of Quadrilaterals
- The sum of the interior angles in a Quadrilateral add up to 360°
- Prove the diagonals of a parallelogram bisect each other
- Questions >
  - Construct a square given one side
Polygons
- Parts of a Polygon
- Types of Polygons
- Questions >
  - How to Construct any Polygon
  - Construct a Hexagon given one side
  - Construct a Hexagon in a given circle
  - How to Construct an Octagon in a Square
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Types of Polygons

Regular Polygons In order to construct any regular polygon you will need to calculate the angle formed between 2 vertices (have to be next to each other) and the centre point of that polygon. (Shown below)

In order to calculate that angle you divide 360 by the number of sides you want on your polygon.360/No. of Sides = Angle at the CenterFor Example if we wanted to construct a Pentagon (5 sides), it would be 360 divided by 5 = to 72° On all regular polygons this angle is also the Exterior angle. If you extend one of the sides through a vertex, then an exterior angle is formed as show below. This is also very useful in constructing polygons.

Equilateral Triangle

Equilateral Triangle - An equilateral triangle is the only triangle that can be classed as a regular polygon because it 3 sides of equal length and 3 angles of equal measure.

Square

Square - A square is the only quadrilateral that can be classed as a regular polygon because its 4 sides are equal in length and the 4 angles are equal in measure.

Pentagon

Pentagon - Is a 5 sided Polygon. The angle required to draw a pentagon is 72°. 360/5=72°

Hexagon

Polygon - Is a 6 sided polygon. The angle required to draw a hexagon is 60° You can also see that a hexagon is made up of 6 equilateral traingles. 360/6=60°

Heptagon

Heptagon - Is a 7 sided polygon. The angle required to draw a heptagon is 51°360/7=51°

Octagon

Octagon - Is an 8 sided polygon. The angle required to draw a Octagon is 45°360/8=45°

Nonagon

Nonagon - Is a 9 sided polygon. The angle required to draw a Nonagon is 40°.360/9=40°

Decagon

Decagon - Is a 10 sided polygon. the angle required to draw a Decagon is 36°360/10=36°

Hendecagon or Undecagon

Undecagon - Is an 11 sided polygon. The angle required to draw a Undecagon is 33°360/11=33°

Dodecagon

Dodecagon - Is a 12 sided polygon. The angle required to construct a Dodecagon is 30°360/12=30°

Irregular Polygons An irregular polygon is any polygon that has differing side lengths and angles of differing measure to all the polygons listed above. Shown below is a couple of examples of irregular polygons.