Unit 3 Review Day 1

1. Unit 3 Review Day 1

2. Agenda • Quiz • Warm-up • Homework Check • Project • Homework

3. Quiz – When finished complete: 1. m< 1 + m<2 = 180. Which lines are parallel and why? 2. If a ll c, b ⊥ a, a. what is m<8? b. what is m<2? Bonus: Find m<1.

4. Project - I Wanna be like M.C. Escher

5. Tessellation Project Today we will discuss the requirements and expectations for your Tessellation projects and you will receive a brief introduction to the different types of tessellations. This is an individual project.

6. Tessellation Project • Maurits Cornelis Escher (1898 – 1972) was a Dutch artist famous for his repetitive, interlocking pattern. His works look like paintings but were done by woodcarving and lithographs. • Escher’s designs are made from variations on tiling patterns called tessellations. A floor covered by square tiles is an example of a tessellation of squares.

7. Tessellations & Transformations Tessellations can be modified by using transformations. As you know, transformations are movements of geometric figures. One transformation, commonly used to create tessellations is a slide, or translation, of a figure.

8. Translation Tessellations For simple translation tessellations, polygons should have opposite sides that are parallel and congruent – squares, hexagons, parallelograms.

9. Example: Translation Tessellation You can create more complex designs starting with square tessellations and making changes on both pairs of sides.

10. Depending how you decide to color your tessellation, a very simple design can have a very creative result.

11. Glide Reflection Tessellation For glide reflection tessellations, polygons should have opposite sides that are parallel and congruent – squares, hexagons, parallelograms.

12. Example By reflecting and gliding over more than one side, you can create a more complex tessellation.

13. Adding coloring and features will enhance the artwork.

14. Tessellation created by Rotation Adjacent sides must be congruent – squares, equilateral triangles, regular hexagons, rhombi

15. Midpoint Rotations • Triangles, Squares, and Quadrilaterals Note: More than one side may be altered for more challenging designs. Coloring one side of the pattern will help prevent accidental flipping during tracing.

16. Example: Rotational Tessellation

18. Suggestions • READ THE Project Sheet first before trying your tessellation. There is a lot of good information in the packet that will help you in deciding on which type of tessellation to do and in creating your tessellation. • Research M.C. Escher • A template that is approximately 2 inches by 2 inches will work well to create an 8 ½ by 11 inch tessellation.

19. Suggestions • Try out several designs, by cutting and taping paper together until you find something you like. • When you have decided on a design, create your template on a stiff material – heavy cardstock or a file folder seem to work well for creating a sturdy template that can be traced over and over. • Be creative. Your design should not look like any of the designs in the packet or in this presentation. • Remember: Finding a design online and copying it is plagiarism.

20. Tessellation Project • Your project is due on Thursday, October 18 at the beginning of class. Grading criteria is in your packet. • On the due date, you must turn in your completed tessellation, your template (attached to the back of your tessellation), your summary paragraph (for each Design), and your assigned packet. • Do NOT wait until the last minute!!!!!

21. Extra Review/Extra Practice Find the missing angle:

26. Homework Review Sheet AND Review sheet of unit 2 – Must complete in order to take retake of unit 2 in Class on Thursday.