pannini’s pizza parlor advertises that you could get a one-topping pizza from them once a week for...

BELLWORK•Pannini’s Pizza Parlor advertises that you could get a one-topping pizza from them once a week for over two years and never have exactly the same pizza twice! Are they correct? Here is their menu

•How many triangles are there in the 4, 5 and 6th triangles if there are 1 in the first, 3 in the second and 6 in the third?

Type of Crust

Sizes Toppings

Thin Small Cheese Pepperoni Chicken Ground Beef Sausage Green PepperOnion Eggplant Sun-Dried TomatoAnchovies Olives MushroomsSpinach Pineapple

Regular Medium

Deep Dish Large

1 2 3 4

BELLWORK SOLUTION•Pannini’s Pizza Parlor advertises that you could get a one-topping pizza from them once a week for over two years and never have exactly the same pizza twice! Are they correct? Here is their menu

Type of Crust

Sizes Toppings

Thin Small Cheese Pepperoni Chicken Ground Beef Sausage Green PepperOnion Eggplant Sun-Dried TomatoAnchovies Olives MushroomsSpinach Pineapple

Regular Medium

Deep Dish Large

BELLWORK SOLUTION•How many triangles are there in the 4, 5 and 6th triangles if there are 1 in the first, 3 in the second and 6 in the third?

1 2 3 4

LINES OF SYMMETRYSection 5.α

The Concept Today we’re going to be talking about a relatively basic topic,

but one that is very important to our discussion of geometry, specifically in regards to areas and three dimensional solids

SYMMETRYLine of Symmetry-Imaginary line drawn that creates a reproduced piece of an

object

SYMMETRYThere are primarily two kinds of lines of symmetry• Bilateral

• Splits the object exactly in half

• Rotational or Radial• Reproduces a piece of the object as it rotates about a

center

SYMMETRYLet’s take a closer look at rotational symmetryInstead of splitting an object up we look to cut it into pieces from

a “center of symmetry”This is done in such a way that each piece replicates itself as it’s

rotated around

EXAMPLEDescribe the kind of symmetry and the angle of rotational

symmetry

EXAMPLESTypically there is at most two ways to divide an object radially,

although there are many ways to do it bilaterally

If we looked at this object

rotationally, how many “pieces” would their be?

EXAMPLEWhat are lines of symmetry for this object

EXAMPLEWhat are bilateral lines of symmetry for this object

EXAMPLEWhat are lines of symmetry for this object

EXAMPLEWhat objects to we see on a daily basis that have lines of

symmetry?

EXAMPLEWhat are lines of symmetry for this object

EXAMPLEWhat are lines of symmetry for this object

EXAMPLEWhat are lines of symmetry for this object

EXAMPLEWhat are lines of symmetry for this object

EXAMPLEWhat are lines of symmetry for this object

EXAMPLEWhat are lines of symmetry for this object

EXAMPLEWhat are lines of symmetry for this object

DRAWINGOne of the ways that lines of symmetry are used is in the

process of drawing objects

For instance

This looks a lot like a reflection…

REGULAR POLYGONSA helpful Theorem for us to remember governs symmetry in

regular polygonsTheorem 5.20: Lines of symmetry in regular polygons

The number of lines of symmetry in a regular n-gon is equal to the number of sides

HOMEWORK

9.61-20, 27-30

MOST IMPORTANT POINTS• Bilateral Symmetry• Radial Symmetry• Drawing using a line of symmetry