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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

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Bellwork

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?

1

2

3

4


Bellwork solution

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


Bellwork solution1

Bellwork Solution

1

2

3

4

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?


Lines of symmetry

Lines of Symmetry

Section 5.α


The concept

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


Symmetry

Line of Symmetry

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

Symmetry


Symmetry1

  • There 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

Symmetry


Symmetry2

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

Symmetry


Examples

Typically there is at most two ways to divide an object radially, although there are many ways to do it bilaterally

Examples


Example

What are lines of symmetry for this object

Example


Example1

What are bilateral lines of symmetry for this object

Example


Example2

What are lines of symmetry for this object

Example


Example3

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

Example


Example4

What are lines of symmetry for this object

Example


Example5

What are lines of symmetry for this object

Example


Example6

What are lines of symmetry for this object

Example


Example7

What are lines of symmetry for this object

Example


Example8

What are lines of symmetry for this object

Example


Example9

What are lines of symmetry for this object

Example


Example10

What are lines of symmetry for this object

Example


Drawing

This looks a lot like a reflection…

One of the ways that lines of symmetry are used is in the process of drawing objects

For instance

Drawing


Regular polygons

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

Regular Polygons


Homework

Homework

9.6

1-20, 27-30 (don’t figure angles)


Most important points

  • Bilateral Symmetry

  • Radial Symmetry

  • Drawing using a line of symmetry

Most Important Points


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