3.1 – polygons and symmetry

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