1. Warm Up
Use the linking cubes to build the polyhedron with these views.
Front Right Side Top
Now, count the faces, edges, and vertices. Count Carefully!! Does Euler’s formula hold up?

2. Agenda Go over warm up Transformations Similarity vs. Congruence
Exploration 9.1
Exploration 9.5
Exploration 9.6
Similarity vs. Congruence
Assign Homework

3. Warm Up
Front Right Side Top
Faces: 9 Edges: Vertices: 14

4. Reflections Miras Look at it--there are two sides.
Flat edge on line of reflection towards pre-image, indented edge toward image.
Look through to find reflection.
Complete the Mira Reflection worksheet.

5. Exploration 9.4 Do part 1 like this in pairs:
Go through 1a - c, and mark where you predict the image to be.
Check with the Mira.
Then, do 1d - f, and mark where you predict the image to be.
Repeat this process for 3a - c, and d - f.
Write sentences about how to estimate reflections at the bottom of the page.

6. Now, use a ruler…
Measure the perpendicular distance from any preimage point to the line of reflection: compare this distance to its respective image point and the line of reflection.
The line of reflection is __?__ of the segment containing any preimage and its respective image.

7. Exploration 9.5
Paper folding--in pairs: your goal is to do Part 2 #1a - h and #2a - h. Do as many as you need in order to write directions for a student to determine what the unfolded paper will look like based on the folded paper diagram.
Write out these directions for Part 3 #1b and 2b. You may include diagrams, color, etc.
Turn in one set of directions per pair.

8. Exploration 9.6
On your own, make predictions for the images of a - i when a 180˚ rotation is made.
Then, use patty paper to check your work.
Then, use a different color and determine the preimage for a 90˚ clockwise rotation.
Write sentences about how to estimate rotations at the bottom of the page.

9. Symmetry and Similarity1 2 3 4 5 6 7 8 9
Warm Up
At the right is a multiplication table with only the ones digit showing. Describe any rotations, translations reflections…

10. Agenda Go over warm up. Discuss types of symmetry Explorations 9.7
More detailed discussion of similarity
Exploration 9.1, 9.12
A brief discussion of tessellations
Assign homework
Get ready for exam.

11. Exploration 9.7 In your groups, 1a only. Name each figure.
Any rotation symmetries?
Any reflection symmetries?
Any you are not sure about???

12. Types of symmetry Translation symmetry/ies Rotation symmetry/ies
Reflection symmetry/ies

13. Tessellations, briefly
This is sometimes called “tiling” the plane.
A figure is repeated in such a way that there are no overlaps and no gaps.

14. 2 1 3 1 3 2

15. How can you tell?
Take any quadrilateral, then rotate it, 180˚. Make some copies of these.

16. Now, put them together.

17. In general The sum of the angles about a point must total 360˚.
So, question: will every convex quadrilateral tessellate?
Will regular hexagons tessellate?
Will regular octagons?

18. Similarity Do exploration 9.1 part 3 on page 239.
Using geoboard paper draw TWO similar figures for a, b, d, f, and g only.
Write a definition or a detailed description of what makes two figures similar.

19. Similarity Figures that are similar have corresponding parts--
The corresponding angles are congruent.
If each of the corresponding sides is also congruent, then the two figures are congruent.
If each of the corresponding sides are in the same proportion, then the two figures are similar.
If even one pair of corresponding sides is not in the same proportion, then the figures are not similar.

20. Just a refresher How do we write this? R L K J I H G F E D C B A Q P NM O

21. Congruent vs. Similar

22. Find missing lengths
4.5 7 3 y 1 x 3

23. If the sun shines on a 6 foot man creating a 10 inch shadow, how long will the shadow be of a 40-foot cactus?
Not to scale