Shapes, Symmetry and Tessellation

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Let’s learn more about shapes, polygon and geometric figures.

A shape is a particular form or appearance of an object. It can be a two- or three-dimensional shape. Shapes can be a polygon. A polygon is a plane figure where the sides are straight and form an angle. A polygon can be regular or irregular. An irregular polygon does not have equal sides and angles. A regular polygon has equal sides and angles.

A regular polygon has straight equal sides and congruent interior angles. There are many types of regular polygon. Here are some examples:

If all sides are congruent and all angles measure 90 degrees, then the regular polygon is a square.

An equilateral triangle is a triangle that has a three equal sides and angles. Its angles measure 60 degrees.

A regular pentagon is a five-sided polygon whose measure of all the angles is 108 degrees, and each side is congruent.

Symmetry is a figure with equal sides and can be divided into similar parts. A line that divides the shape into similar parts is called the line of symmetry. If we draw the line of symmetry between the shape to satisfy the condition, then the shape has symmetry. The line of symmetry can be a vertical, horizontal or diagonal line. Let’s take an isosceles triangle cut by a line of symmetry.

The vertical line that divides a triangle is the line of symmetry or axis of symmetry. If the triangle is folded along the line of symmetry and matches exactly, then the triangle is symmetrical.

A rectangle has more than one line of symmetry – a vertical and a horizontal line. A line of symmetry in a figure can be more than one as long as it cuts the figure in similar parts. A circle has infinite symmetry.

Some shapes have rotational symmetry. Rotational symmetry is when we rotate the figure to its centre point and it looks exactly like the original shape.

Tessellation in a plane is tiling one or more geometric figures. If we put together a figure in an infinite number, leaving no gaps or overlaps, then it is tessellated.

Example: The square is tessellated leaving no gaps. It can be other shapes as long as it does not overlaps and has no gaps.