Geometry Opener(s) 3/16
3/16
It’s Curlew Day, Freedom of Information Day, Goddard Day,
Goddard Day, Lips Appreciation Day, National Artichoke
Hearts Day, National Everything You Do Is Right Day and
National Panda Day!!! Happy Birthday Jhene Aiko, James
Madison, George Ohm, Pat Nixon, Jerry Lewis, Jerry Jeff
Walker, Alice Hoffman, Nancy Wilson, Flavor Flav and
Isabelle Huppert!!!
3/16
What to do today:
1. Do the opener.
2. [Period 8: Complete mastery tracker.]
3. Watch a dilation video using compass.
4. Dilate a playing card using compass.
5. Listen to a lecture about grades.
6. Graph and dilate shapes on coordinate plane.
7. Look at a PPT slide describing coordinate plane
dilation.
8. Investigate measurements of image/pre-image.
9. Watch a negative scale factor dilation video.
10. Begin HW.
11. Do the exit pass.
TODAY’S OPENER
Agenda
1. Opener (5)
2. [Period 8: Mastery Tracker] (5)
3. Video: Dilation Method 2 (10)
4. Ind. Work: Roll For It Card Dilation (35)
5. Lecture: Grades Update (10)
6. Ind. Work 2: Graphing & Dilating 3 Shapes (10)
7. PPT: Dilation Method 3 (5)
8. Investigation: Shape Measurements (5)
9. Video 2: Dilating a Negative Scale Factor (5)
10. HW Time: Text ?s, p. 772, Lesson 9-5 (10)
11. Exit Pass (5)
PCQ is the
image of YCZ.
Determine the
scale factor and
whether it is a
reduction,
enlargement or
congruency transformation.
http://www.onlinemathlearning.com/dilation-transformation.html
Standard(s)
 CCSS-HSG-CO.C.9: Prove theorems about lines and
angles…when a transversal crosses parallel lines, alternate
angles are congruent and corresponding angles are congruent.
 CCSS-HSG-GPE.B.5: Use the slope criteria for parallel and
perpendicular lines and use them to solve geometric problems.
 CCSS-HSG-SRT.1: Verify experimentally the properties of
dilations given a center and a scale factor.
 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.
Essential Question(s)




How Do I (HDI) find missing  measures using ICCE 
concepts?
HDI write linear equations?
HDI characterize || and  lines in terms of slope?
HDI dilate a figure using a center and scale factor?
Objective(s)





Students will be able to (SWBAT) correlate anti-blobbiness
with geometry.
SWBAT name and identify || lines, transversals and ICCE
angles.
SWBAT determine missing ICCE angle measures, using
postulates/theorems and/or algebra.
SWBAT use slope to write a linear equation.
SWBAT dilate a figure given a center and scale factor.
THE LAST OPENER
A dilation maps triangle LMN to triangle L'M'N'.
MN = 14 in. and M'N' = 9.8 in. If LN = 13 in., what
is L'N' ?
In the white space of your blown-up letter, make the following
measurements, do the following calculations and answer the
following questions. It would be wise to label the points of
your blow-up…the vertices (corners)…with prime notation
first!:
1. Measure the two longest sides of your letters, both image
and pre-image. Pick two DIFFERENT long side lengths.
2. Use those measurements to calculate your ACTUAL scale
factor or factors. (Use the formula from your notes the day
before yesterday.) Realize these numbers might be different
than the one you answered your opener with.
3. Are your two scale factors EXACTLY the same?
4. Did you create a TRUE dilation? Why yes or why no?
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. 772, Lesson 9-5
HOMEWORK Period 7
Text ?s, p. 772, Lesson 9-5
HOMEWORK Period 3
Text ?s, p. 772, Lesson 9-5
HOMEWORK Period 5 and 8
Text ?s, p. 772, Lesson 9-5
HOMEWORK Period 2A
Text ?s, p. 772, Lesson 9-5
Extra Credit
Period 1 Period 2A Period 3
Israel H. (9x)
Jose C. (10x)
Mirian S. (6x)
Perla S. (3x)
Melissa A.
Israel A. (6x)
Benito E.
Amal S. (6x)
Stephanie L.
(8x)
Alexis S. (4x)
Evelyn A. (7x)
Daniela G.
Yesenia M.
Yazmin C. (3x)
Joe L. (3x)
Safeer A.
Kevin G.
Isabel G. (3x)
Roxana M. (3x)
Alex H. (3x)
Victor C. (4x)
Frank S.
Alondra Z.
1.
Jaime A. (5x)
Nadia L. (6x)
Anthony P.
Griselda Z. (5x)
Jaclyn C. (3x)
Brandon S.
(10x)
Mayra C. (2x)
Jacob L. (4x)
Leo G.
Alejandra G.
Mayra G.
Rodrigo F. (2x)
Anthony C.
Josh P. (7x)
Ana O. (4x)
Fabian (4x)
Noemi O.
Paul P. (2x)
Gabino G.
Carolyn D.
Sonia T. (3x)
Amanda S. (5x)
Josue A. (6x)
Arslan A. (5x)
Angie H.
Paulina G. (3x)
Alicia R. (4x)
Ricardo D. (3x)
Rosie R. (2x)
Ronny V. (2x)
Gaby O. (2x)
Alex A. (2x)
Claudia M. (2x)
Angie H. (4x)
Jocelyn J.
Omar G.
Michelle S. (4x)
Alex A.
Period 5
Period 7
Period 8
Antonio B.
(11x)
Rogelio G. (9x)
Eraldy B. (5x)
Anthony G.
(4x)
Alex A. (3x)
Brianna T. (3x)
Jose B. (12x)
Carlos L. (9x)
Anadelia G.
(4x)
Jose D. (5x)
Cesar H. (3x)
Saul R.
Alex A.
Jose C. (8x)
Solai L.
Jorge L.
Liz L. (2x)
Rob C.
Adriana H. (9x)
Jackie B. (6x)
Jose R. (10x)
Julian E. (6x)
Jocelyn C. (13x)
Jenny Q.
Ruby L. (5x)
Ana R. (6x)
V. Limon (3x)
Zelexus R.
Kamil L. (3x)
Diego P. (3x)
Alfredo F. (3x)
Lilliana F. (5x)
Christian A. (2x)
Liz A. (2x)
Carmen A. (7x)
Brenda B. (3x)
Julian E. (2x)
Jennifer G. (5x)
Gaby G. (2x)
Jessica T. (5x)
Jorge C. (3x)
Gerardo L. (2x)
Val R. (2x)
Gerardo L.
Esme V. (3x)
Alejandra P.
Cynthia R.
Xavier G. (3x)
Maria M. (4x)
Fernando V. (4x)
Stephanie E.
Oscar S. (2x)
Andrea N. (2x)
Kevin A.
Saul O. (2x)
Jose G.
Lily 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/
ICCE Lines and Equations Poster Rubric
What I’m Looking For
What You Can Get What You Got
3 Characteristics
1 Problem-Solving Reminder
5 Problem-Solving Steps
3 Reasons
3 Stained Glass Graphs
a. Colored
b. Labeled Lines
c. White-outed Lines
Overall neatness / beauty /
readability
3 pts.
1 pt.
5 pts.
3 pts.
3 pts.
3 pts.
3 pts.
3 pts.
12 pts.
TOTAL
36 pts.
ICCE Lines and Equations Poster Rubric
What I’m Looking For
What You Can Get What You Got
3 Characteristics
1 Problem-Solving Reminder
5 Problem-Solving Steps
3 Reasons
3 Stained Glass Graphs
c. Colored
d. Labeled Lines
d. White-outed Lines
Overall neatness / beauty /
readability
3 pts.
1 pt.
5 pts.
3 pts.
3 pts.
3 pts.
3 pts.
3 pts.
12 pts.
TOTAL
36 pts.
CORRESPONDING ICCE ANGLES
Corresponding 
1
CHARACTERISTICS:
2
1. They eat crackers in bed while watching TV.
2. They share the same colored clothes.
3. They have skinny legs.
4. ???
1 and 2 in the stained glass window to the
left are Corresponding s!
When you solve
a Corresponding
s problem,
take away their
crackers and put
purple leggings
on them.
1
Given:
m1=[some expression with x]
m2=[some expression with x]
Find:
x, m1 and m2
2
The s to the right are
Corresponding because:
1. They have legs that look like toothpicks.
2. They have cracker crumbs in their beds.
3. They are both wearing red scarves.
4. ?????
[Show the work
and solutions]
1 = 80°
2 = 80°
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