Bellwork

1. 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? Bellwork 1 2 3 4

2. 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 Solution

3. 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

4. Section 5.α Lines of Symmetry

5. 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

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

7. 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

8. 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

9. Describe the kind of symmetry and the angle of rotational symmetry Example

10. 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? Examples

11. What are lines of symmetry for this object Example

12. What are bilateral lines of symmetry for this object Example

13. What are lines of symmetry for this object Example

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

15. What are lines of symmetry for this object Example

16. What are lines of symmetry for this object Example

17. What are lines of symmetry for this object Example

18. What are lines of symmetry for this object Example

19. What are lines of symmetry for this object Example

20. What are lines of symmetry for this object Example

21. What are lines of symmetry for this object Example

22. 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

23. 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

24. 9.6 1-20, 27-30 Homework

25. Bilateral Symmetry • Radial Symmetry • Drawing using a line of symmetry Most Important Points