S Y M M E T RY, A S W I D E O R A S N A R R O W A S Y O U M AY D E F I N E I T S M E A N I N G, I S O N E I D E A BY W H I C H
M A N T H R O U G H T H E A G E S H A S T R I E D T O C O M P R E H E N D A N D C R E AT E O R D E R , B E A U T Y A N D
P E R F E C T I O N.
— H E R M A N N W E Y L , 1 8 8 5 - 1 9 5 5 ( G E R M A N - A M E R I C A N M AT H E M AT I C I A N )
3.1 – Polygons and Symmetry
Test Corrections
Explain why the original answer was incorrect
Show work/provide justification for the correct answer
Staple to testReturn by Friday15 points (HW and a half)After school TODAY
Do Now
What do all of these letters have in common?A H I T V X
Name another letter that belongs in the groupWhat do these letters have in common?
B C D E K
How are the two groups related?
Polygons
Review: A polygon is a plane figure formed from three
or more segments such that each segment intersects exactly two other segments, one at each endpoint, and no two segments with a common endpoint are collinear.
Key points: Three or more segments Each segment intersects two and only two other
segments at endpoints No two segments lie on the same line
Classifying Polygons by # of Sides
Name # of Sides Name # of SidesTriangle 3 Nonagon 9Quadrilateral 4 Decagon 10Pentagon 5 11-gon 11Hexagon 6 Dodecagon 12Heptagon 7 13-gon 13Octagon 8 n-gon n
The prefix indicates the number of sides
Other classifications
Equilateral: all segments have equal measure Examples:
Equiangular: all angles have equal measure Examples: http://www.cut-the-knot.org/Curriculum/Geometry/
EquiangularPoly.shtml#Explanation
Regular Polygons
Regular polygons are both equilateral and equiangular
Reflectional Symmetry
Think “Mirror Image”A figure has reflectional symmetry if and
only if its reflected image across a line coincides exactly with the preimage. The line is called an axis of symmetry
Alphabet Reflections
Which (capital) letters of the alphabet have reflectional symmetry?
Triangles
Take a look at the triangles on your notes Scalene; Isosceles; Equilateral
Draw in any axes of symmetry you can findWhich triangles have reflectional symmetry?
Rotational Symmetry
An object has rotational symmetry if and only if it has at least one rotation image, not counting rotations of 0° or multiples of 360°, that coincides with the original.
We describe an objects rotational symmetry by naming how many “rotational images” it has.
2-fold5-fold
6-fold
Rotational Symmetry Examples
How many –fold symmetry do regular octagons have? Heptagons? n-gons?
How many degrees will each rotation by in a regular polygon’s rotational symmetry?
http://www.analyzemath.com/Geometry/rotation_symmetry.html
Which Symmetry?
A.ReflectionalB.Rotational
Something to think about…
What objects can you think of that have either reflectional or rotational symmetry?
Is that symmetry essential to the object’s function?
Are there any objects that need to be unsymmetrical?
HOMEWORK: pg. 142 – 4, 7, 11-14, 23, 27-29, 33-39, 62