Symmetry

Learning Objectives Identify reflectional (line) symmetry in two-dimensional figures. Draw all lines of symmetry for a given geometric shape. Determine if a figure has rotational symmetry and identify its center of rotation. Calculate the order and angle of rotational symmetry for a figure. Describe the relationship between symmetry and rigid transformations (reflections and rotations). Complete a figure given one part of it and a line of symmetry. Have you ever noticed how a butterfly's wings are perfect mirror images of each other? 🦋 That's symmetry in action! In this tutorial, we will explore the geometric property of symmetry. You will learn about two main types: reflectional (or line) symmetry and rotational symmetry. Understanding symmetry helps us describe...

TermDefinitionExample SymmetryA property of a geometric figure where the figure remains unchanged after a transformation, such as a reflection or rotation, is applied to it.A square has symmetry because it looks the same after being rotated 90° or reflected across a line through its center. Reflectional Symmetry (Line Symmetry)A figure has reflectional symmetry if it can be divided by a line into two parts that are mirror images of each other.A heart shape has one vertical line of symmetry down its middle. Line of SymmetryThe imaginary line that divides a figure with reflectional symmetry into two identical, reflected halves.A rectangle has two lines of symmetry: one that runs horizontally through its middle and one that runs vertically through its middle. Rotational SymmetryA figure has...

Angle of Rotational Symmetry Formula Angle = \frac{360^{\circ}}{\text{Order}} Use this formula to find the smallest angle of rotation when you know the order of rotational symmetry. The order is the number of times the shape fits onto itself in a full turn. Order of Rotational Symmetry Formula Order = \frac{360^{\circ}}{\text{Angle}} Use this formula to find the order of rotational symmetry when you know the smallest angle of rotation that maps the figure onto itself.