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Tessellations

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Tessellations

Study Guide

Key Definition

A tessellation is a repeated geometric design that covers a plane without any gaps, spaces, or overlaps.

Important Notes

A square can tessellate a plane.
An equilateral triangle can tessellate a plane.
Any triangle or parallelogram can tessellate a plane.
A regular pentagon cannot tessellate a plane without gaps.
Multiple shapes can be combined to tessellate a plane.

Mathematical Notation

$\angle$ represents the interior angle of a polygon

Remember to use proper notation when solving problems

Why It Works

Tessellations work because they use shapes that fit together without gaps, covering the entire plane.

Remember

Any triangle or parallelogram can tessellate a plane because they can be repeated without gaps.

Quick Reference

Tessellation Property:Shapes that can cover a plane without gaps

Understanding Tessellations

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A simple explanation: tessellations are patterns with no gaps using shapes like squares or triangles.

Practice Problems

Test your understanding with practice problems

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine designing a tiled floor. Which shapes should you use to cover the floor completely without gaps? $\text{Think of the options}$

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider a pattern using hexagons. Can they tessellate a plane on their own? $\text{Explain your reasoning}$

Challenge Quiz

Single Choice Quiz

Advanced

Which combination of shapes can tessellate a plane? $\text{Select one}$

Recap

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Review key concepts and takeaways