- If a figurehas pointsymmetryit has rotationalsymmetry.
- The converseis not true. If a figurehas rotationalsymmetryit may, or may not, havepointsymmetry.
Manyflowershavepetalsthat are arrangedin pointsymmetry. (Keepin mindthat someflowershave
petals.Theydonothavepointsymmetry. See the next example.)
Hereis a figurethat has rotationalsymmetrybut not pointsymmetry.
Planesof Symmetry
Three-dimensional(3-D)figuresalso havesymmetry. Theycan haveline or pointsymmetry, just as two-
dimensionalfigurescan.
A 3-D figurecan also haveone or moreplanesof symmetry.
Aplaneof symmetrydividesa 3-D figureinto two partsthat are reflectionsof eachotherin the plane.
The planecuts throughthe cylinderexactlyhalfwayup the cylinder. It is a planeof symmetryfor the cylinder.
Noticethat this cylinderhas manymoreplanesof symmetry. Everyplanethat is perpendicularto the top
baseof the cylinderand containsthe centerof the baseis a planeof symmetry.
The planein the diagramaboveis theonlyplaneof symmetryof the cylinder, that is parallelto the base.
Example 1
How manyplanesof symmetrydoesthe rectangularprismbelowhave?