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?

Agenda• Go over warm up• Transformations

– Exploration 9.1 – Exploration 9.5– Exploration 9.6

• Similarity vs. Congruence• Assign Homework

Warm Up• Front Right Side Top

Faces: 9 Edges: 21 Vertices: 14

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.

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.• Check with the Mira.• Repeat this process for 3a - c, and d - f.• Write 2 - 3 sentences about how to estimate reflections

at the bottom of the page.

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.

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.

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 2 - 3 sentences about how to estimate

rotations at the bottom of the page.

Symmetry and Similarity• Warm Up• At the right is

a multiplicationtable with only the ones digitshowing.Describe any rotations, translationsreflections…

1 2 3 4 5 6 7 8 9

1 1 2 3 4 5 6 7 8 9

2 2 4 6 8 0 2 4 6 8

3 3 6 9 2 5 8 1 4 7

4 4 8 2 6 0 4 8 2 6

5 5 0 5 0 5 0 5 0 5

6 6 2 8 4 0 6 2 8 4

7 7 4 1 8 5 2 9 6 3

8 8 6 4 2 0 8 6 4 2

9 9 8 7 6 5 4 3 2 1

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.

Exploration 9.7• In your groups, 1a only.

– Name each figure.– Any rotation symmetries?– Any reflection symmetries?– Any you are not sure about???

Types of symmetry• Translation symmetry/ies

• Rotation symmetry/ies

• Reflection symmetry/ies

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.

3

2 13

21

How can you tell?• Take any quadrilateral, then rotate it,

180˚. Make some copies of these.

• Now, put them together.

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?

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.

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.

Just a refresher• How do we write this?

ORL

K J

I

HG

F

E D

C

BA

Q P

NM

Congruent vs. Similar

Find missing lengths

3

4.5

7

7

3

y1

x7

• 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