Download Keys GEO SY14-15 Openers 2-5

Geometry Opener(s) 2/5
2/5
It’s National Weatherperson’s Day, Wear Red Day,
World Nutella Day, Primrose Day, Disaster Day,
Bubble Gum Day and National Chocolate Fondue
Day!!! Happy Birthday Bobby Brown, Laura Linney,
Jennifer Jason Leigh, Barbara Hershey, Errol Morris,
Hank Aaron, Red Buttons, William S. Burroughs and
Adlai Stevenson!!!
2/5
What to do today:
1. Do the opener.
2. Watch a video.
3. Practice rotating with spinning/protractor.
4. Watch a video.
5. Practice rotating with 3 steps.
6. Take some double entry journal notes.
7. Take some PPT notes.
8. Practice rotational symmetry
9. Start HW.
10. Do the exit pass.
TODAY’S OPENER
1.
Agenda
1. Opener (15)
2. REGULAR: Model 1: Rotation with No Tracing
Paper (5)
https://www.youtube.com/watch?v=Foe8VFKAB8Y
3. Practice: With Spinning (15)
4. HONORS: Model 2: Rotation with Protractor &
Point (5)
https://www.youtube.com/watch?v=U4Hv494HwrQ
5. Practice: With Protractor (15)
6. Model 3: Rotation w/out Protractor & Point (5)
https://www.youtube.com/watch?v=FqiGuTtjmMg
7. Practice: Rotation in 3 Steps (15)
8. Notes 1: Rotational Symmetry – Text, p. 478
Double Entry Journal (10)
9. Notes 2: Rotational Symmetry – PPT (5)
10. Practice: Wksht. 9-3, p. 492 (10)
11. HW Time: Selected problems
12. Exit Pass (15)
Standard(s)
 CCSS-M-G-CO.2: Represent transformations in the plane using
tracing paper, functions, etc.
 CCSS-M-G-CO.5: Given a geometric figure and a rotation,
reflection or translation, draw the transformed figure using, e.g.,
graph paper, tracing paper or geometry software.
 CCSS-M-G-CO.6: Use descriptions of rigid motions to transform
figures.
Essential Question(s)


How Do I (HDI) transform images?
HDI transform images within the coordinate plane?
Objective(s)



Students will be able to (SWBAT) correlate anti-blobbiness
with geometry.
SWBAT transform images using measurement or other
methods.
SWBAT transform images within the coordinate plane.
Decide on one person from your group to get a piece of graph
paper for each member and your group’s tool box.
2. Create a BIG coordinate plane.
3. Plot the following triangle: B(0,0) I(10,0) G(10,8)
4. Label it with 3 non-collinear points on the vertices.
5. Draw a sketch on your opener paper and label it.
6. Now, rotate the triangle 90° and 180° counterclockwise around the
origin. Use your formulas.
7. Draw a sketch on your opener paper and label it.
8. Draw, measure (in cm) and label the following segments with the
measurements: ̅̅̅̅
𝑰𝑶, ̅̅̅̅
𝑰′𝑶 , ̅̅̅̅
𝑮𝑶, ̅̅̅̅̅
𝑮′𝑶 [ O = (0,0) … the origin ]
9. Get a protractor and measure the following angles and label them
with degrees: IOI’ and GOG’
10. Can you make a conjecture about spins / rotations? Write your
conjecture on your opener paper.
THE LAST OPENER
11. One person from your group get a piece of graph paper for each
member and your group’s tool box.
12. Create a BIG coordinate plane.
13. Take out a protractor.
14. Put the straight edge of the inner semicircle along the positive xaxis.
15. Place the left ‘vertex’ of the semicircle on the origin.
16. Trace it and label it with 3 non-collinear points: 2 on the vertices
and 1 at the top of the semicircle.
17. Draw a sketch on your opener paper and label it.
18. Now, spin your protractor 90° clockwise around the origin.
19. Trace it and label it.
20. Draw a sketch on your opener paper and label it.
21. Do the same for TWO (2) more 90° spins.
22. Can you make a conjecture about spins / rotations? Write your
conjecture on your opener. (HINT: Use a ruler!)
Exit Pass (12/11 – 13/14)
For numbers 1-6 find the coordinates of each
image.
1. Rx-axis (A)
2. Ry-axis (B)
3. Ry = x (C)
4. Rx = 2 (D)
5. Ry= -1 (E)
6. Rx = -3 (F)
The Last Exit Pass
HOMEWORK Period 1
Text ?s, p. 480, #14-15, #22-24
HOMEWORK Period 7
Kuta Rotations Wksht. [Redo p. 1 w/non-origin spin points:
#1. (2,-2) #2. (-2,-2) #3. (-2,2) #4. (2,2) #5. (1,1) #6. (-1,1)
HOMEWORK Period 3
Text ?s, p. 480, #22-24
HOMEWORK Period 5 and 8
Kuta Rotations Wksht.
HOMEWORK Period 2A
Text ?s, p. 480, #22-24
Extra Credit
Period 1 Period 2A Period 3
Israel H.
Jose C.
Mirian S. (2x)
1.
Jaime A. (2x)
Nadia L.
Anthony P.
Griselda Z.
Jaclyn C.
Brandon S.
Sonia T.
Amanda S.
Josue A.
Period 5
Period 7
Antonio B. (2x)
Rogelio G. (2x)
Eraldy B.
Anthony G.
Alex A.
Brianna T.
Jose B.
Carlos L.
Adriana H.
Jackie B.
Jose R. (2x)
Julian E.
Jocelyn C. (2x)
Jenny Q.
Ruby L.
Ana R.
Watch a portion of RHYTHmetric video (“What are the 3 ‘laymen’s’ terms for 3 of our 4 transformations?”).
http://www.youtube.com/watch?v=NKtJd1hkI9k
http://www.youtube.com/watch?v=V9uYcnjlAks
http://www.youtube.com/watch?v=X1xPZjItmDk%20
http://www.shodor.org/interactivate/activities/Transmographer/
Period 8
Jessica T. (2x)
Jorge C.
Gerardo L.
Val R.
Gerardo L.
Esme V.
Tessellation Rubric
Name
Period
What I’m looking for
What it’s worth
Tessellation Image Construction
Recognizable: 6 pts.
Almost recognizable: 5 pts.
Almost recognizable but incomplete: 4
Unrecognizable: 2 pts.
Clearly identifiable figure due to markings: 6 pts.
Identifiable but incomplete…or minimally detailed: 5 pts.
Semi-identifiable figure: 4 pts.
No figure: 3 pts.
Multiple colors fill image: 6 pts.
More than 1 color but primarily 1: 5 pts.
Single color fills image/Alternating color pattern: 4 pts.
Single color fills image: 3 pts.
Bits of color spottily used: 2 pts.
No color used: 1 pt.
Images ‘lock’: 6 pts.
Images partially ‘lock’: 2 pts.
Images do not ‘lock’: 1 pts.
Incredible: 6 pts.
Intriguing…almost fascinating…adorable: 5 pts.
Interesting…cute: 4 pts.
Typical…unoriginal: 3 pts.
Minimalist: 2 pts.
 14 boxes by 20 boxes: 6 pts.
< 14 boxes by 20 boxes: 2 pts.
Tessellation Image Figure
Tessellation Image Coloring
Tessellation Image ‘Locking’
Tessellation Image Creativity
Tessellation Size
Total
Tessellation Rubric
36 pts.
Name
Period
What I’m looking for
What it’s worth
Tessellation Image Construction
Recognizable: 6 pts.
Almost recognizable: 5 pts.
Almost recognizable but incomplete: 4
Unrecognizable: 2 pts.
Clearly identifiable figure due to markings: 6 pts.
Identifiable but incomplete…or minimally detailed: 5 pts.
Semi-identifiable figure: 4 pts.
No figure: 3 pts.
Multiple colors fill image: 6 pts.
More than 1 color but primarily 1: 5 pts.
Single color fills image/Alternating color pattern: 4 pts.
Single color fills image: 3 pts.
Bits of color spottily used: 2 pts.
No color used: 1 pt.
Images ‘lock’: 6 pts.
Images partially ‘lock’: 2 pts.
Images do not ‘lock’: 1 pts.
Incredible: 6 pts.
Intriguing…almost fascinating…adorable: 5 pts.
Interesting…cute: 4 pts.
Typical…unoriginal: 3 pts.
Minimalist: 2 pts.
 14 boxes by 20 boxes: 6 pts.
< 14 boxes by 20 boxes: 2 pts.
Tessellation Image Figure
Tessellation Image Coloring
Tessellation Image ‘Locking’
Tessellation Image Creativity
Tessellation Size
Total
What you get
36 pts.
What you get
Today’s Worksheets Rubrics
Line of Symmetry Wksht.
#2. 2 pts.
50 %  at least 3 pts.
#3. 2 pts.
64%  at least 6 pts.
#4. 2 pts. (Correctly identifying 5 letters with 76%  at least 9 pts.
lines of symmetry; correctly identifying 5
88%  at least 12 pts.
letters with NO lines of symmetry)
93%  at least 15
#5. 6 pts. (1 for each image)
100%  18
#6. 4 pts. (1 for each image WITH the
specified # of lines of symmetry)
#7. 2 pts. (Yes with an example to support
‘yes’ or no with counterexample to support
‘no’)
Reflections Wksht.
#1. 8 pts. (1 for each ? or gap fill)
#2. 7 pts. (1 for each instruction or request to
write a statement)
#3. 4 pts. (1 for each image)
#4. 5 pts. (1 for each instruction; 2 for the
entire path)
50 %  at least 4 pts.
64%  at least 8 pts.
76%  at least 12 pts.
88%  at least 16 pts.
93%  at least 20
100%  24
Reflections on a Coordinate Plane Wksht.
#2. 8 pts. (1 for each table entry and ?)
50 %  at least 6 pts.
#3. 7 pts. (1 for each table entry and ?)
64%  at least 12 pts.
#4. 9 pts. (1 for each table entry, ? and
76%  at least 18 pts.
labeling the image)
88%  at least 24 pts.
#5. 12 pts. (1 for each set of pre-image & 93%  at least 30
image coordinates; 2 for each set of
100%  36
formulaic coordinates [in the boxes!])
Copying & Bisecting a Segment
Copying a Segment
1.
2.
3.
4.
5.
Draw a segment.
Label its endpoints I and F.
Draw another non-collinear point.
Label it E.
Draw an arc in your segment
from 1 endpt. to the other. (Don’t
change your compass’s width!)
6. Draw the same arc starting from
point E.
7. Label a point on the second arc N.
8. Connect E to N.
Bisecting a Segment
1. Place your compass point on E.
2. Place your pencil point at least
̅̅̅̅ and draw a
halfway across 𝑬𝑵
half-circle arc. (Don’t change your
compass’s width!)
3. Place your compass point on N.
4. Draw the exact same halfcircle arc. (Don’t change your
compass’s width!)
5. Label the arc intersection points
T and H.
6. Connect T to H.
Copying & Bisecting an Angle
Copying an Angle
1. Draw a ray.
2. Label its endpoint U.
3. Draw another non-collinear ray
that shares the 1st ray’s endpt.
4. Draw another separate ray…
far away from the angle.
5. Label its endpt. L
6. Draw an arc in your  from 1
side to the other. (Don’t
change your compass’s width!)
7. Label the intersection points B and G.
8. Draw the same arc on your
3rd ray.
9. Label its intersection point Y.
10.Draw a 2nd arc in your  with compass pt.
on G and pencil point on B. (Don’t change
your compass’s width!)
11.Draw the same arc on your 3rd ray.
12.Label the intersection point F.
13.Connect L to F.
Bisecting an Angle
1. Draw an angle.
2. Label its vertex A.
3. Draw an arc in your angle
from one side to the other.
4. Label the intersection pts. W and P.
5. Draw an arc with your compass pt.
on W, at least ½ -way across the
interior. (Don’t change your
compass’s width!)
6. Draw the same arc from your P.
7. Label the intersection point of
those 2 arcs S.
8. Connect A to S.
YOUR PROOF CHEAT SHEET
IF YOU NEED TO WRITE A PROOF ABOUT
ALGEBRAIC EQUATIONS…LOOK AT THESE:
Reflexive
Property
Symmetric
Property
Transitive
Property
Addition & Subtraction
Properties
Multiplication &
Division Properties
Substitution
Property
Distributive
Property
IF YOU NEED TO WRITE A PROOF ABOUT
LINES, SEGMENTS, RAYS…LOOK AT
THESE:
For every number a, a = a.
Postulate 2.1
For all numbers a & b,
if a = b, then b = a.
For all numbers a, b & c,
if a = b and b = c, then a = c.
For all numbers a, b & c,
if a = b, then a + c = b + c & a – c = b – c.
For all numbers a, b & c,
if a = b, then a * c = b * c & a ÷ c = b ÷ c.
For all numbers a & b,
if a = b, then a may be replaced by b in any
equation or expression.
For all numbers a, b & c,
a(b + c) = ab + ac
Postulatd 2.2
Postulate 2.3
Postulate 2.4
Postulate 2.5
Postulate 2.6
Postulate 2.7
The Midpoint
Theorem
IF YOU NEED TO WRITE A PROOF ABOUT THE
LENGTH OF LINES, SEGMENTS, RAYS…LOOK
AT THESE:
Reflexive
Property
Symmetric
Property
Transitive
Property
Addition & Subtraction
Properties
Multiplication &
Division Properties
Substitution
Property
Segment Addition
Postulate
Through any two points, there is exactly ONE
LINE.
Through any three points not on the same
line, there is exactly ONE PLANE.
A line contains at least TWO POINTS.
A plane contains at least THREE POINTS not on
the same line.
If two points lie in a plane, then the entire line
containing those points LIE IN THE PLANE.
If two lines intersect, then their intersection is
exactly ONE POINT.
It two planes intersect, then their intersection
is a LINE.
If M is the midpoint of segment PQ, then
segment PM is congruent to segment MQ.
IF YOU NEED TO WRITE A PROOF ABOUT
THE MEASURE OF ANGLES…LOOK AT
THESE:
AB = AB
(Congruence?)
If AB = CD,
then CD = AB
If AB = CD and CD = EF,
then AB = EF
If AB = CD,
then AB  EF = CD  EF
If AB = CD,
then AB */ EF = CD */ EF
If AB = CD,
then AB may be replaced by CD
If B is between A and C, then AB + BC = AC
If AB + BC = AC, then B is between A and C
Reflexive
Property
Symmetric
Property
Transitive
Property
Addition &
Subtraction
Properties
Multiplication &
Division Properties
Substitution
Property
m1 = m1
(Congruence?)
If m1 = m2,
then m2 = m1
If m1 = m2
and m2 = m3, then m1 = m3
If m1 = m2,
then m1  m3 = m2  m3
DEFINITION OF
CONGRUENCE
Whenever you change from
 to = or from = to .
If m1 = m2,
then m1 */ m3 = m2 */ m3
If m1 = m2,
then m1 may be replaced by m2
IF YOU NEED TO WRITE A PROOF ABOUT ANGLES IN GENERAL…LOOK AT THESE:
Postulate 2.11
The  Addition
Postulate
Theorem 2.5
The Equalities Theorem
If R is in the interior of PQS,
then mPQR + mRQS = mPQS.
THE CONVERSE IS ALSO TRUE!!!!!!
Q
Congruence of s is

Reflexive, Symmetric & Transitive
P
R
S
Theorem 2.8
Vertical s
Theorem
If 2 s are vertical, then they are .
(1  3 and 2  4)
IF YOU NEED TO WRITE A PROOF ABOUT COMPLEMENTARY or SUPPLEMENTARY ANGLES
…LOOK AT THESE:
Theorem 2.3
Supplement
Theorem
If 2 s form a linear pair,
then they are
supplementary s.
Theorem 2.4
Complement
Theorem
If the non-common sides of
2 adjacent s form a right ,
then they are complementary s.
Theorem 2.12
 Supplementary
Right s Therorem
Theorem 2.6
R The  Supplements
Theorem
S
P Q
Q
P
If 2 s are  and supplementary, then each
 is a right .
Theorem 2.7
The  Complements
R Theorem
S
Theorem 2.13
 Linear Pair Right
s Therorem
s supplementary to the
same  or to  s are .
(If m1 + m2 = 180 and
m2 + m3 = 180, then 1  3.)
s complementary to the
same  or to  s are .
(If m1 + m2 = 90 and
m2 + m3 = 90, then 1  3.)
If 2  s form a linear pair, then they
are right s.
YOUR PROOF CHEAT SHEET (continued)
IF YOU NEED TO WRITE A PROOF ABOUT RIGHT ANGLES or PERPENDICULAR LINES…LOOK AT THESE:
Theorem 2.9
Perpendicular lines
Theorem 3-4
If a line is  to the 1st of two || lines,
Perpendicular Transversal Theorem
4 Right s Theorem
intersect to form 4 right s.
then it is also  to the 2nd line.
Theorem 2.10
Postulate 3.2
All right s are .
2 non-vertical lines are  if and only if the PRODUCT of their
Right  Congruence Theorem
Slope of  Lines
slopes is -1. (In other words, the 2nd line’s slope is the 1st line’s
slope flipped (reciprocal) with changed sign.)
Theorem 2.11
Perpendicular lines
Postulate 3.2
If 2 lines are  to the same 3rd line, then thhose 2
 Adjacent Right s Theorem
form  adjacent s.
 and || Lines Postulate
lines are || to each other.
Theorem 4-6
Theorem 4-7
If the 2 legs of one right  are  to
If the hypotenuse and acute  of one right
Leg-Leg (LL) Congruence
Hypotenuse-Angle
the corresponding parts of another
 are  to the corresponding parts of
(HA) Congruence
right , then both s are .
another right , then both s are .
Theorem 4-8
Postulate 4-4
If the hypotenuse and one leg of one right
If the leg and acute  of one right  are
Leg-Angle (LA)  to the corresponding parts of another
Hypotenuse-Leg (HL)
 are  to the corresponding parts of
Congruence
Congruence
another right , then both s are .
right , then both s are .
IF YOU NEED TO WRITE A PROOF ABOUT ICCE ANGLES or PARALLEL LINES…LOOK AT THESE:
Postulate 3.1
If 2 || lines are cut by a
Postulate 3.4
If 2 lines are cut by a transversal
Corresponding Angles
transversal, then each pair of CO
Corresponding Angles/|| Lines
so that each pair of CO s is ,
Postulate (CO s Post.)
s is .
Postulate (CO s/|| Lines Post.) then the lines are ||.
Theorem 3.1
If 2 || lines are cut by a
Theorem 3.5
If 2 lines are cut by a transversal so
Alternate Interior Angles
transversal, then each pair
Alternate Exterior Angles/|| Lines
that each pair of AE s is , then the
Theorem (AI s Thm.)
of AI s is .
Theorem (AE s/|| Lines Thm.)
lines are ||.
Theorem 3.2
If 2 || lines are cut by a
Theorem 3.6
If 2 lines are cut by a transversal
Consecutive Interior Angles
transversal, then each pair
Consecutive Interior Angles/|| Lines so that each pair of CI s is
Theorem (CI s Thm.)
of CI s is supplementary.
Theorem (CI s/|| Lines Thm.)
supplementary, the lines are ||.
Theorem 3.3
If 2 || lines are cut by a
Theorem 3.7
If 2 lines are cut by a transversal so
Alternate Exterior Angles transversal, then each pair
Alternate Interior Angles/|| Lines that each pair of AI s is , then the
Theorem (AE s Thm.)
of AE s is .
Theorem (AI s/|| Lines Thm.)
lines are ||.
Postulate 3.2
2 non-vertical lines have the same
Postulate 3.5
If you have 1 line and 1 point NOT on that
Slope of || Lines
slope if and only if they are ||.
|| Postulate
line, ONE and only ONE line goes through
that point that’s || to the 1st line.
Theorem 6.6
Theorem 6.4
A midsegment of a  is || to one
In ACE with ̅̅̅̅̅
𝑩𝑫 || ̅̅̅̅
𝑨𝑬 and
 Midsegment Thm.

Proportionality
Thm.
intersecting
the
other 2 sides in distinct
side of the , and its length is ½
̅̅̅̅
𝑩𝑨 ̅̅̅̅
𝑫𝑬
the length of that side.
points, = .
̅̅̅̅
𝑪𝑩
̅̅̅̅
𝑪𝑫
Postulates and Theorems to IDENTIFY CONGRUENT TRIANGLES: SSS, ASA, SAS or AAS
Postulates and Theorems to IDENTIFY SIMILAR TRIANGLES: AA, SSS or SAS
Linear Equation in
Slope-Intercept
Form
Linear Equation in
Point-Slope Form
y = mx + b
m = slope, b = yintercept
y – y1 = m(x – x1)
m = slope,
(x1, y1) = 1 point on
the line
Linear Equation in Standard Form
Ax + By = C
I – Numbers and coefficients can only be Integers. (No fractions or decimals.)
P – The x coefficient must be Positive. (A > 0)
O – Zero can only appear beside a variable Once. (If A = 0, then B ≠ 0)
D – Numbers and coefficients can only be Divisible by 1. (GCF = 1)
S – Variables can only be on the Same side of the equal sign.
CI s: 2 inside || lines on SAME side of transversal.
CO s: 1  inside || lines & 1  outside || lines, on OPPOSITE sides of transversal.
AI s: 2 inside || lines on OPPOSITE sides of transversal.
AE s: 2 outside || lines on OPPOSITE sides of transversal.
AE
CO
AI
CO
CI
AE
AI/
CI