Unit 1 Class Notes - Rigid Transformations

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Rigid Transformations
Geometry Unit 1
Graphing Coordinate Pairs
Plot (4,4), (5,0), (4,-4)
( x-coordinate , y-coordinate )
( horizontal ↔, vertical ↕ )
Graphing Coordinate Pairs
Plot (0,5), (0,-5), (-4,4)
(-5,0), (-4,-4)
Connect all eight dots with lines to make a shape
Check with partners
Graphing Coordinate Pairs
Plot & Connect (2,-2), (0,-3), (-2,-2)
Plot (2,1), (-2,1)
Check with partners
On ruled side of index card, please print:
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Your first and last name.
What you like to be called.
Sports you play.
Extra-curriculars you participate in (church choir,
drama production, etc.)
If and where you work. Hours & days?
Your dream profession.
A reasonable back-up profession, as you see it.
Do you have reliable home/cell internet access?
1. Please complete the Get-to-Know-You index
card.
2. Detach pages 3-4 from signed syllabus &
remove staple.
3. Keep pp. 1-2, have pp. 3-4 on desk to turn in.
4. If not yet signed, get it in tomorrow.
5. Reminder: No food, drink, gum, headphones,
iPods, Gameboys... Cells silenced. Water okay.
Graphing Coordinate Pairs
On whiteboards, plot and connect to make five shapes:
Shape 1: (2,2), (2,4), (4,4), (5,2)
Shape 2: (-2,2), (-5,2), (-5,4), (-3,4)
Shape 3: (-2,-4), (-5,-4) (-5,-2), (-3,-2)
Shape 4: (2,-2), (5,-2), (4,-4), (2,-4)
Shape 5: (8,3), (8,6), (10,6), (10,4)
Label the shapes. Check with partners.
Rigid Transformations
Talk with your partners about how to:
1. Turn Shape 1 into Shape 2.
2. Turn Shape 1 into Shape 3.
3. Turn Shape 1 into Shape 4.
4. Turn Shape 1 into Shape 5.
Write answers on the back of the whiteboard.
To Avoid Textbook Fines…
1. In pen, write your first & last name and 2014-2015
inside front cover.
2. In margin on page 11, write in pen the barcode
number of book from the back cover, in case it falls
off.
3. Keep textbook at home. We have a class set.
Now please read instructions for the Battleship! game.
1. Place materials on desk for HW check:
2. On whiteboard, plot, connect & label:
Shape 1: (2,1), (-2,4), (1,6)
Shape 2: (3,7), (6,9), (7,4)
Note: Polygons are shapes with straight sides.
Rigid Transformation
• Shape stays the same, doesn’t bend, flex, shrink
or grow.
• Can prove with patty paper.
• Can prove with ‘algebra rules.’
• Can prove with compass & protractor.
Translation
• Translation is a rigid transformation that slides
the shape.
• May be in the x- or y-direction, or both.
• Can use two patty papers to translate along a
Line of Translation (LoT).
• Can use an ‘algebra rule’ to translate. What are
these rules?
Reflection
• Reflection is a rigid transformation that mirrors a
shape across a line of reflection (LoR).
• Can use one folded patty paper to reflect.
• Can use an ‘algebra rule’ to reflect. What are
these rules?
Translation & Reflection Practice
• 7 min - With your partners, answer Q’s 1-3, pp.
362 in notebook.
• Be prepared to present.
Translation & Reflection Practice
• With your partners, answer Q’s 4, 5, 11, pp. 362363 in notebook. Be prepared to present.
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Warm Up
Have notebook open to show HW for check.
Grab a class textbook for each pair.
Read about symmetry, pp. 3-4.
After discussing with partners, answer Q’s 4-8
in your notebook.
Symmetry = Balanced on both sides
Reflectional Symmetry = Can fold one side of a
shape perfectly over the other side.
Line of Reflection (LoR)
Rotational Symmetry = As the shape rotates, it
looks the same at several points on a 360o spin.
Three Points of
Rotational
Symmetry
Http://www.mathsisfun.com/geometry/symmetry-reflection.html
http://indiandigitalartists.com/wp-content/uploads/2013/08/Composition-in-Photography-Symmetry-and-Pattern-2.jpg
http://www.unframedworld.com/wp-content/uploads/2011/06/symmetry-photo-how-to02.jpg
1. 20 min - With your partners, complete Quiz 1.
Mr. Sidman will be around to give feedback.
2. If you would like to show Mr. Sidman a much
improved HW from yesterday, please have it
out.
3. Discuss two Q’s of your choice from quiz.
4. 20 min – Practice rotations of polygons.
5. Answer HW Q #4 using patty paper…
On whiteboard, draw polygon with corners
(2,2), (2,4), (4,4), (6,2)
Now rotate this around origin 90o, 180o, 270o.
That’s one pre-image and three images.
Repeat, using (1,3) as your Point of Rotation
(PoR).
1. Have HW out for check.
2. Grab one textbook per group.
3. With partners, complete practice quiz 1.
4. When all agree, complete practice quiz 2.
5. Students will be asked to write their HW & quiz
answers on the board and explain them to the
class.
Coordinate Pair Rules
1. Adding or subtracting from x translates left or
right.
2. Adding or subtracting from y translates up or
down.
(x,y) → (x+2,y-3)
Coordinate Pair Rules
1. Making x negative reflects across y-axis.
2. Making y negative reflects across x-axis.
(x,y) → (x,-y)
Coordinate Pair Rules
5. Making x and y negative reflects across both
axes…which is really a 180o rotation around
origin.
(x,y) → (-x,-y)
• Get out Take-Home Quiz Handout + Notebook
on Rigid Transformations
• Get out red or green grading pen
• Row 1 switch notebook/quiz with Row 2
• Row 3 switch notebook/quiz with Row 4
• If no one behind you, switch with neighbor
• Once you switch, write “Graded by: your name”
at top of quiz handout
Find-Your-Match Game
• Find other people with cards that match yours:
term, definition, sketch (picture), symbol
• Write information for all group’s cards under
correct term on board
• Get out HW for check.
• Grab one textbook per team.
• With your partners, complete the Symbol
Practice handout.
• Students will be placing HW answers on the
board and explaining them to the class.
• I will finish stamping practice handout and we
will go over answers.
• 10 min - With your partners, complete the
Symbol Practice handout.
• I will finish stamping practice handout while you
take quiz.
• 30 min – Quiz. Notes o.k. Solo, individual effort.
Notes:
• Naming and sketching angles
• Describing congruent angles in symbols and
sketches
• Measures of segments and angles
• Angle bisectors in sketches and symbols
• Reflecting rays: Incoming angle  Outgoing angle
• Grade Friday quiz & discuss
• Correct your own practice handout from last
week
• Have HW out for check
• Grab one textbook per team
• Students will present answers
• Discovery video on rigid transformations &
graphic design
• Intro to extra credit HW project
• Practice fire drill (if time)
1. Grab one whiteboard, dry-erase marker and rag
per person.
2. Plot pre-image: (-6, -4), (-2, -3), (-4, -7)
3. Plot image: (2, 3), (4, 7), (6, 4)
4. Is this a rigid transformation or not?
Can use patty paper, on back shelf.
5. Write all the reasons for your answer on board.
6. If it is a rigid transformation, write the type.
7. If it is a rigid transformation, write a ‘rule’ for it.
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Advanced Topics in Transformations Unit
How to calculate slopes of lines.
If slopes stayed the same between pre-image
and image, shape did not reflect or
rotate…only translated.
How to calculate distance between points on
Cartesian plane (using the Pythagorean
Theorem)
If side lengths stay the same, shape did not
grow or shrink.
1. We are going to calculate the lengths of all
sides in both shapes.
x-distance between points = x2 – x1 = 5 – 1 = 4
y-distance between points = y2 – y1 = 5 – 2 = 3
1. To calculate the length of a side:
x-distance between points = x2 – x1 = 5 – 1 = 4
y-distance between points = y2 – y1 = 5 – 2 = 3

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