triangle and quadrilateral tessellations

a ppt is here

• angle properties from a triangular tessellation
• completing a triangle tessellation
• quadrilateral tessellations are also 180 rotations about the mid-points (must they be?)
• seeing the basis ('skeleton') for a tessellation

with some of the angles on the grid labelled:
(a , b or c)

you can see what
e.g. the angle sum of a particular hexagon is

what are the angles in a complete turn?
(2a + 2b + 2c)

in half a turn?

what happens to the angles on parallel lines?

to complete a tessellation of triangles maybe encourage students to identify the sets of parallel lines - so that their tessellations go right to the edges of the space provided

the triangles above have been chosen so that they can be rotated (180 degrees) about the mid-points of the sides

for quadrilaterals:

every tessellation of a quadrilateral is a disguised tessellation of parallelograms

which is a tessellation of the triangle that is half of the parallelogram

there are various 'skeleton' (as David Wells calls them) tessellations of parallelograms that can be discerned

the easiest to 'see' is the one that joins corresponding corners - based on the vectors that they translate through to generate the tessellation

hinged tessellation by Al Grant

there are several interactive versions,

the corners of which can be adjusted