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 6 th triangles if there are 1 in the first, 3 in the second and 6 in the third? Type of CrustSizesToppings ThinSmallCheese PepperoniChicken Ground BeefSausageGreen Pepper OnionEggplant Sun-Dried Tomato AnchoviesOlivesMushrooms SpinachPineapple RegularMedium Deep DishLarge 1234

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 CrustSizesToppings ThinSmallCheese PepperoniChicken Ground BeefSausageGreen Pepper OnionEggplant Sun-Dried Tomato AnchoviesOlivesMushrooms SpinachPineapple RegularMedium Deep DishLarge

How many triangles are there in the 4, 5 and 6 th triangles if there are 1 in the first, 3 in the second and 6 in the third? 1234

Section 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

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

There are primarily two kinds of lines of symmetry BilateralBilateral Splits the object exactly in halfSplits the object exactly in half Rotational or RadialRotational or Radial Reproduces a piece of the object as it rotates about a centerReproduces a piece of the object as it rotates about a center

Let’s take a closer look at rotational symmetry Instead 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

Describe the kind of symmetry and the angle of rotational symmetry

Typically 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?

What are lines of symmetry for this object

What are bilateral lines of symmetry for this object

What are lines of symmetry for this object

What objects to we see on a daily basis that have lines of symmetry?

What are lines of symmetry for this object

One 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…

A helpful Theorem for us to remember governs symmetry in regular polygons Theorem 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

, 27-30

Bilateral SymmetryBilateral Symmetry Radial SymmetryRadial Symmetry Drawing using a line of symmetryDrawing using a line of symmetry