Symmetry
If a shape has a line of symmetry, the line of symmetry will divide the shape
into two equal parts, one half of which can be folded along the line of symmetry
to fit exactly onto the other. Note, a rectangle has two (not four) lines of
symmetry and a circle has an infinite number. If rotating a shape through a
certain angle produces an identical shape, it has rotational symmetry. If the
shape can be rotated 4 times before returning to its original shape (e.g. a
square), it has "rotational symmetry of order 4". An equilateral triangle has
rotational symmetry of order 3 and a rectangle has rotational symmetry of order
2.
Triangles
Isosceles triangles have two equal angles. The sides of the triangle opposite
the equal angles are equal in length to one another. Equilateral triangles
have all of their sides and angles equal. Since there are 180 degrees in a
triangle and all the angles are equal, each angle is 60 degrees.
Other Shapes
Parallelogram: opposite sides are parallel, opposite angles
are equal, the diagonals bisect one another. Rhombus: (a parallelogram with
all four sides of equal length), diagonals bisect one another at right
angles. Trapezium: One pair of opposite sides are parallel. Square: All
sides are equal, all angles are 90 degrees, diagonals bisect one another at 90
degrees. Rectangle: All angles are 90 degrees, diagonals bisect one
another.
Tessellation
A shape is said to tessellate if an infinite number of that
shape can be put together, leaving no gaps. For example, a square
tessellates:
Other shapes which tessellate include equilateral triangles
and hexagons. Shapes can also tessellate with one another, for example
equilateral triangles and squares tessellate with one another:
Copyright © Matthew Pinkney 2003
