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
Faces: 9
Right Side
Top
Edges: 21
Vertices: 14
Reflections
• Miras
– Look at it--there are two sides.
– Flat edge on line of reflection towards preimage, 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
1
Similarity
• Warm Up
• At the right is
a multiplication
table with only
the ones digit
showing.
Describe any
rotations,
translations
reflections…
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
1
2
1
2
3
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?
A
B
G
H
M
N
O
R
F
C
E
D
L
I
K
J
Q
P
Congruent vs. Similar
Find missing lengths
4.5
7
x
7
3
3
7
y
1
• 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