Questions and Answers in the Lab 9 Patterns

Pattern 0

This pattern has only translations, no rotation, reflections or glide reflections.

• Pick two of the basic triangle tiles that are at some distance apart and tell what the translation is as a product of T_AB and T_AD.
• Write the product in a different order and trace the triangle again. Since translations commute, you should end up the same place.

Pattern 1

• Look for halfturns that are products of two line reflections.
• Look at translations. The horizontal and vertical ones are products of 2 parallel line reflections. Is this true for a "diagonal" translation (not same row or same column? Why?
• Look at translations again, as products of half turns. Are diagonals also products of half turns?
• Look for glide reflections as triple line reflections.

Pattern 2

Look for half turn centers. Also the isosceles right triangles.

Why are there no glide reflections?

Pattern 3

Look for translations that are the products of 90 and 270 rotations.

Look for glide reflections that are the products of 90 rotation and line reflection.

One big idea

Isometry is determined by values on 3 non-collinear points. There can't be two.