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Use translations and reflections in tessellations

Geometry: Master Shapes, Proofs & Spatial Reasoning

Angles and Lines

Angle relationships

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Parallel and perpendicular line segments

Identifying Parallel Lines

Identifying Perpendicular Lines

Perpendicular bisectors

Angle bisectors

Angle Bisectors

Coordinate Plane

Cartesian plane

Cartesian Plane — Coordinates

Draw on coordinate planes

Triangles

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Classifying Triangles

Isosceles and Equilateral Triangles

Circles

Angles in a circle

Chord properties 

Tangent properties

Circles and circumference 

Circle properties

Arcs of a circle

Areas and sectors of circles

Central angles and proofs

Inscribed angles and proofs

Central and inscribed angles in circles

Circle chord, tangent, and inscribed angles proofs

Surface Area and Volume

Volume of rectangular prisms word problems

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Introduction to volume

Calculate the Volume

Volume of prisms

Find the volume

Volume of Prisms Calculate Area and Volume

Rectangular Prisms Table

Volume of Prisms — Word Problem

Volume of cylinders

Word problems relating volume of prisms and cylinders

Surface area of cylinders

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Transformations

Identifying vertices

Line symmetry

Rotational symmetry and transformations

Understanding tessellations

understand tessellations Interior Angle

Tessellations using translations and reflections

tessellations using translations and reflections

Tessellations using rotations

Introduction to transformations

Horizontal and vertical distances

Similarity

Similar solids

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Congruence

Congruence and congruent triangles

Triangles congruent by SSS proofs

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

Logic

Inductive reasoning

Statements

Negations

Conjunctions and disjunctions

Truth tables

Conditionals

Inverses, converses, and contrapositives

Biconditionals

Deductive reasoning

Algebraic proofs

Reasoning

Consecutive integers

Number sequences

Finding the missing digit

math

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-geometry.png

Ex. 1:

Ex. 2:

Counting reflection symmetries of a regular hexagon

<p>- [Instructor] Hi, welcome to the question right here. So what can we do, what type of transformation can we do to get this tessellation? Well, if you look at it.you can actually choose let's say reflection. My first answer is, I'm going to pick my reflection. The reason I pick my reflection is because I can simply take this whole thing right here, do you see that? I can pick this as one figure. Then, I'm just going to reflect it to the left. That's it. Reflect it on the Y axis, it works. I can also reflect on the X axis which is over here. See, if I reflect it down I get the exact same graph. I can reflect it here, I get the exact same graph, okay? Well, is that the only choice I have? No, what about translation? Have you ever done translation before?<br />
Translation just means that you can move it left and right. So that is I just pick this whole thing right here, the first one right here. Pick it up, translate to the right, I also get the same graph or the same pattern. So that way, I can create my tessellation using the reflection also using the translation. Both method will get you the answer for sure. Oh I'm sorry, will get you the tessellation, okay? In terms of the last one, the transformation I'm probably thinking that it may not work by looking at it. It may or may not. Okay? Because I can't really see it by rotating just the yellow-- No we have to do the yellow and the gray at the same time. So it looks like that there's no room for your rotation. So just these two will be your final answer. Okay? Thanks for watching.</p>


Identifying reflection, translation, and rotation in a tessellation

Identifying reflection and translation in a tessellation pattern

Identifying translation as the transformation for a tessellation

Translations and reflections are two of the few ways of how tessellations are created. We will use a tile as an example here. Reflection means flipping over the tile by its edge. On the other hand, translation means picking the tile up and putting it down to the space originally next to it.

Tessellations using translations and reflections

What You'll Learn

Identify reflection, translation, and rotation transformations in tessellation patterns

Determine which transformations create specific tessellations without gaps

Recognize how reflection flips tiles across axes to form repeating patterns

Apply translation by sliding tiles to adjacent positions in tessellations

Count reflection symmetries in regular polygons like hexagons

What You'll Practice

Identifying transformations used in given tessellation diagrams

Determining whether reflection, translation, or rotation works for specific patterns

Counting lines of symmetry in regular polygons

Analyzing which transformations create gap-free tessellations

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

4 Video lessons

Practice exercises

Skills

Tessellations

Transformations

Reflection

Translation

Rotation

Symmetry

Geometry