8. Polygons

Exercises

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Polygons

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When line segments are connected in succession so that the end point of the first segment becomes the starting point of the next segment, the result is a polygonal chain. If the start and end points of the polygonal chain converge, a closed polygonal chain is formed.

Definitions related to polygons

A polygon is a part of a plane bounded by a closed, non-self-intersecting polygonal chain.
The diagonal of a polygon connects two non-adjacent vertices.
The angle of a polygon is the angle between two sides whose opening is inside the polygon.

Polygons are named by listing the vertices of the polygon in order. A polygon can also be named by the number of vertices, angles, or sides in it. For example, a hexagon has 6 vertices, 6 angles, and 6 sides.

Example 1

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a) pentagon
b) dodecagon
c) hexagon
d) triangle
e) quadrilateral
f) square
g) decagon

Quadrilaterals

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Let’s take a closer look at the quadrilaterals next. Some quadrilaterals have their own designations.

Definitions related to quadrilaterals

A quadrilateral is a non-intersecting, closed polygonal chain of four segment lines
A trapezium is a rectangle whose two sides are parallel.
A parallelogram is a rectangle with two pairs of parallel sides.
A rectangle is a parallelogram with one right angle
A rhombus or diamond is a parallelogram with two adjacent sides of equal length.
A square can be defined in two ways:
- 1) A rectangle with two adjacent sides of equal length.
- 2) A rhombus with one right angle.

Example 2

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Let’s look at the following figures and their definitions.

All of the patterns are quadrilaterals.
Although only b looks like a trapezium, c, d, e and f also fulfill the criteria of a trapezium.
The quadrilaterals c, d, e and f are parallelograms.
Figures d and f are rectangles.
Figures e and f are rhombuses.
The definition of a square is only seen in figure f.

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