Why five-sided figures pose a problem, from Professor John Hunton - and a bit about the importance of Penrose Tiling. Professor Hunton works at the University of Leicester. Aligned to Common Core State Standards: 8.G.1, 8.G.2, 8.G.3, 8.G.4, 8.G.5
5 and Penrose Tiling - Numberphile
Verify experimentally the properties of rotations, reflections, and translations:
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.