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Tessellations Using Translations and Reflections
See how sliding (translating) and flipping (reflecting) a shape lets it repeat endlessly to cover a flat surface with no gaps or overlaps.
What You'll Learn
A tessellation is a pattern of shapes that covers a flat surface completely with no gaps or overlaps
Translating a shape means sliding it the same distance and direction repeatedly to build a tessellation
Reflecting a shape flips it across a line; combining reflections with translations creates glide reflections
Squares, equilateral triangles, and regular hexagons are the only regular polygons that tessellate alone
Checking the angle sum around each vertex is the key test for whether a pattern truly tessellates
What You'll Practice
1
Identifying transformations used in given tessellation diagrams
2
Determining whether reflection, translation, or rotation works for specific patterns
3
Counting lines of symmetry in regular polygons
4
Analyzing which transformations create gap-free tessellations
Why This Matters
Tessellations appear everywhere in art, architecture, and naturefrom tile floors to honeycomb patterns. Understanding how transformations create these repeating designs builds your spatial reasoning skills and connects geometry to real-world design and engineering applications.
Before You Start — Make Sure You Can:
This Unit Includes
4 Video lessons
Practice exercises
Learning resources
Skills
Tessellations
Transformations
Reflection
Translation
Rotation
Symmetry
Geometry
NY Curriculum Aligned