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Rotational Symmetry

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Rotational Symmetry

Study Guide

Key Definition

A figure has rotational symmetry if it can be rotated by some angle $0° < θ < 360°$ such that the image coincides with the preimage.

Important Notes

A regular hexagon has an angle of rotation of $60^\circ$.
The order of rotational symmetry for a hexagon is $6$.
A scalene triangle does not have rotational symmetry.
The angle of rotation is the smallest angle for which the figure coincides with itself.
The order of symmetry is how many times a figure aligns with itself in $360^\circ$.

Mathematical Notation

$\angle$ represents an angle

$\triangle$ represents a triangle

$\cong$ represents congruence

Remember to use proper notation when solving problems

Why It Works

By finding the smallest rotation angle that maps a figure onto itself and counting how many such rotations fit into 360°, we can characterize its rotational symmetry.

Remember

Rotational symmetry is identified by the smallest angle and number of rotations using $360^\circ$.

Quick Reference

Angle of Rotation for Hexagon:$60^\circ$

Order of Symmetry for Hexagon:$6$

Understanding Rotational Symmetry

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Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A figure has rotational symmetry if it looks the same after a rotation of less than $360^\circ$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the angle of rotation for a regular hexagon? (Consider a regular hexagon: a six-sided polygon with equal sides.)

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you are designing a logo that needs to have rotational symmetry with an angle of 45^\circ. How many times will it coincide with itself in a full turn? (e.g., an evenly spaced 8-pointed star.)

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Determine the order of rotational symmetry for a regular pentagon that coincides with itself every 72^\circ rotation.

Challenge Quiz

Single Choice Quiz

Advanced

Which polygon has an order of rotational symmetry of 8? (Consider a regular octagon.)

Recap

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Review key concepts and takeaways