Transcript a – b - Haverford School District

Honors Geometry
Spring 2012
Ms. Katz
Day 1: January 30th
Objective: Form and meet study teams. Then work together to
build symmetrical designs using the same basic shapes.
• Seats and Fill out Index Card (questions on next slide)
• Introduction: Ms. Katz, Books, Syllabus,Homework Record,
Expectations
• Problems 1-1 and 1-2
• Möbius Strip Demonstration
• Conclusion
Homework: Have parent/guardian fill out last page of syllabus
and sign; Problems 1-3 to 1-7 AND 1-15 to 1-18; Extra credit
tissues or hand sanitizer (1)
Respond on Index Card:
1.
2.
3.
4.
When did you take Algebra 1?
Who was your Algebra 1 teacher?
What grade do you think you earned in Algebra 1?
What is one concept/topic from Algebra 1 that Ms. Katz
could help you learn better?
5. What grade would you like to earn in Geometry?
(Be realistic)
6. What sports/clubs are you involved in this Spring?
7. My e-mail address (for teacher purposes only) is:
Support
• www.cpm.org
–
–
–
–
Resources (including worksheets from class)
Extra support/practice
Parent Guide
Homework Help
• www.hotmath.com
– All the problems from the book
– Homework help and answers
• My Webpage on the HHS website
– Classwork and Homework Assignments
– Worksheets
– Extra Resources
Quilts
1-1: First Resource Page
1-1: Second Resource Page
Write
sentence
and
names
around
the gap.
Cut
along
dotted
line
Glue sticks are rewarded when 4 unique symmetrical designs
are shown to the teacher.
Day 2: January 31st
Objective: Use your spatial visualization skills to investigate reflection.
THEN Understand the three rigid transformations (translations,
reflections, and rotations) and learn some connections between them.
Also, introduce notation for corresponding parts.
•
•
•
•
•
•
Homework Check and Correct (in red) – Collect last page of syllabus
LL – “Graphing an Equation”
Problems 1-47 to 1-53
Problems 1-59 to 1-62
LL – “Rigid Transformations”
Conclusion
Homework:
Problems 1-54 to 1-58 AND 1-63 to 1-67; GET
SUPPLIES; Extra credit tissues or hand sanitizer (1)
A Complete Graph
•
y = -2x+5
Create a table of x-values
x -4 -3 -2 -1 0 1 2 3 4
y 13 11 9 7 5 3 1 -1 -3
•
•
•
y
10
5
-10
-5
y = -2x+5
5
-5
Use the equation to find
-10
y-values
Complete the graph by scaling and labeling
the axes
Graph and connect the points from your
table. Then label the line.
10
x
Day 3: February 1st
Objective: Begin to develop an understanding of reflection symmetry. Also,
learn how to translate a geometric figure on a coordinate grid. Learn that
reflection and reflection symmetry can help unlock relationships within a
shape (isosceles triangle). THEN Learn about reflection, rotation, and
translation symmetry. Identify which common shapes have each type of
symmetry.
•
•
•
•
•
•
Homework Check and Correct (in red)
LL – “Rigid Transformations”
Problems 1-68 to 1-72
Problems 1-87 to 1-91
LL – “Slope-Intercept Form” and “Parallel and Perpendicular Lines”
Conclusion
Homework:
Problems 1-73 to 1-77 AND 1-82 to 1-86; GET
SUPPLIES; Extra credit tissues or hand sanitizer
Transformation (pg 34)
Transformation: A movement that preserves size and shape
Reflection: Mirror
image over a line
Translation: Slide in a direction
Rotation: Turning about
a point clockwise or
counter clockwise
Everyday Life Situations
Here are some situations that occur in everyday life. Each one
involves one or more of the basic transformations: reflection,
rotation, or translation.
State the transformation(s) involved in each case.
a.
b.
c.
d.
e.
f.
You look in a mirror as you comb your hair.
While repairing your bicycle, you turn it upside down and spin
the front tire to make sure it isn’t rubbing against the frame.
You move a small statue from one end of a shelf to the other.
You flip your scrumptious buckwheat pancakes as you cook
them on the griddle.
The bus tire spins as the bus moves down the road.
You examine footprints made in the sand as you walked on the
beach.
Day 4: February 2nd
Objective: Learn how to classify shapes by their attributes using Venn
diagrams. Also, review geometric vocabulary and concepts, such as
number of sides, number of angles, sides of same length, right angle,
equilateral, perimeter, edge, and parallel. THEN Continue to study the
attributes of shapes as vocabulary is formalized. Become familiar with
how to mark diagrams to help communicate attributes of shapes.
•
•
•
•
•
•
Homework Check and Correct (in red)
Finish Problems 1-89 to 1-91
LL – Several entries
Problems 1-97 to 1-98
Problems 1-104 to 1-108
Conclusion
Homework:
Problems 1-92 to 1-96 AND 1-99 to 1-103; Get Supplies!
Chapter 1 Team Test Monday
Symmetry
Symmetry: Refers to the ability to perform a transformation without
changing the orientation or position of an object
Reflection Symmetry: If a shape has reflection symmetry, then it
remains unchanged when it is reflected across a line of
symmetry. (i.e. “M” or “Y” with a vertical line of reflection)
Rotation Symmetry: If a shape has rotation symmetry, then it can
be rotated a certain number of degrees (less than 360°) about
a point and remain unchanged.
Translation Symmetry: If a shape has translation symmetry, then it
can be translated and remain unchanged. (i.e. a line)
1-72
B
A
A’
Isosceles Triangle
Sides: AT LEAST
two sides of
equal length
Base Angles:
Have the same
measure
Height: Perpendicular
to the base AND splits
the base in half
Reflection across a Side
The two shapes MUST meet at a side that
has the same length.
Polygons (pg 42)
Polygon: A closed figure made up of straight
segments.
Regular Polygon: The sides are all the same
length and its angles have equal measure.
Line: Slope-Intercept Form (pg 47)
y = mx + b
Slope
Slope: Growth or rate of change.
y-intercept
y
m
x
y-intercept: Starting point on the y-axis. (0,b)
Slope-Intercept Form
3
y  x 3
2
You
Next,
use
rise
Firstcan
plotgo
the
Now
connect
backwards
if
over
run towith
plot
y-intercept
on
the
points
new
thepoints
y-axis
anecessary!
line!
Parallel Lines (pg 47)
Parallel lines do not intersect.
Parallel lines have the same slope.
For example:
5
y  x 4
2
and
5
y   x 1
2
Perpendicular Lines (pg 47)
Perpendicular lines intersect at a right angle.
Slopes of perpendicular lines are opposite
reciprocals (opposite signs and flipped).
For example:
2
3
y   x  5 and y  x  1
2
3
Venn Diagram
#1: Has two or
more siblings
#2: Speaks at least
two languages
Venn Diagrams (pg 42)
Condition #1
Condition #2
Satisfies
condition 2
only
Satisfies
condition 1
only
A
B
C
Satisfies
neither
condition
Satisfies both
conditions
D
Problem 1-98(a)
#1: Has at least one
pair of parallel sides
#2: Has at least two
sides of equal length
Problem 1-98(a)
Has at least one pair
of parallel sides
Both
Has at least two
sides of equal length
Neither
Problem 1-98(b)
Has only three sides
Both
Has a right angle
Neither
Problem 1-98(c)
Has reflection
symmetry
Both
Has 180° rotation
symmetry
Neither
Describing a Shape
Shape Toolkit
Shape Toolkit
Day 5: February 3rd
Objective: Continue to study the attributes of shapes as vocabulary is
formalized. Become familiar with how to mark diagrams to help
communicate attributes of shapes. THEN Develop an intuitive
understanding of probability, and apply simple probability using the
shapes in the Shape Bucket.
•
•
•
•
•
Homework Check and Correct (in red)
Wrap-Up Problems 1-107 to 1-108
Problems 1-115 to 1-119
Closure Problems CL1-126 to 1-134 [Choose problems you need to
work on as individuals]
Conclusion
Homework:
Problems 1-110 to 1-114 AND 1-121 to 1-125; Supplies!
Chapter 1 Team Test Monday
Probability (pg 60)
Probability: a measure of the likelihood that an event will
occur at random.
Number of Desired Outcomes
P  event  
Total Possible Outcomes
Example: What is the probability of selecting a heart
from a deck of cards?
Number of Hearts
13 1
P  select a heart  

  0.25  25%
Total Number of Cards 52 4
Shape Bucket
Day 6: February 6th
Objective: Assess Chapter 1 in a team setting. THEN Learn how
to name angles, and learn the three main relationships for angle
measures, namely supplementary, complementary, and
congruent. Also, discover a property of vertical angles.
•
•
•
•
Homework Check and Correct (in red)
Chapter 1 Team Test (≤ 45 minutes)
Start Problems 2-1 to 2-7
Conclusion
Homework:
Problems 2-8 to 2-12
Chapter 1 Individual Test Friday
2-2
A
C’
B
B’
C
a. mA  mB  mC
b.
6
c. mCAC or mCAC
Day 7: February 7th
Objective: Learn how to name angles, and learn the three main
relationships for angle measures, namely supplementary, complementary,
and congruent. Also, discover a property of vertical angles. THEN Use
our understanding of translation to determine that when a transversal
intersects parallel lines, a relationship exists between corresponding
angles. Also, continue to practice using angle relationships to solve for
unknown angles.
•
•
•
•
•
Homework Check and Correct (in red)
Finish Problems 2-1 to 2-7
Problems 2-13 to 2-17
Start Problems 2-23 to 2-28
Conclusion
Homework:
Problems 2-18 to 2-22 AND 2-29 to 2-33
Chapter 1 Individual Test – Is Thursday okay instead?
Notation for Angles
F
E
D
Name
DEF
or
FED
If there is only one angle at the
vertex, you can also name the
angle using the vertex: E
Y
W
X
Z
?
Incorrect:
X
?
Measure
mDEF  45
Correct:
mA  mB
Incorrect:
DEF  45
A  B
Angle Relationships (pg 76)
Complementary Angles: Two
angles that have measures that
add up to 90°.
30°
x°
60°
y°
x° + y° = 90°
Supplementary Angles: Two angles
that have measures that add up
to 180°.
Example: Straight angle
Congruent Angles: Two angles that
have measures that are equal.
Example: Vertical angles
70°
110°
x° y°
x° + y° = 180°
85°
85°
x°
y°
x° = y°
Marcos’ Tile Pattern
How can you create a tile pattern with a single
parallelogram?
Marcos’ Tile Pattern
a. Are opposite angles of a parallelogram
congruent?
Pick one parallelogram on your paper. Use color
to show which angles have equal measure. If
two measures are not equal, make sure they are
different colors.
Marcos’ Tile Pattern
b. What does this mean in terms of the
angles in our pattern? Color all angles that
must be equal the same color.
Marcos’ Tile Pattern
c. Are any lines parallel in the pattern? Mark
all lines on your diagram with the same
number of arrows to show which lines are
parallel.
Marcos’ Tile Pattern
J
a
L
c
w
N
y
b
M
d
x
P
z
K
Use the following diagram to help answer
question 2-15.
Why Parallel Lines?
53°
x
2-16
X
X
2-23 (a)
a
b
More Angles formed by Transversals
132° 48°
48° 132°
132° 48°
48° 132°
>
>
a. Alternateb.Interior(1) Same Side
(2) Interior
(3)
Day 8: February 8th
Objective: Discover the triangle angle sum theorem, and practice finding
angles in complex diagrams that use multiple relationships. THEN Learn
the converses of some of the angle conjectures. Also, apply knowledge of
angle relationships to analyze the hinged mirror trick from Lesson 2.1.1.
•
•
•
•
•
Homework Check and Correct (in red)
Review Chapter 1 Team Test & Algebra Review
Finish Problems 2-26 to 2-28
Problems 2-43 to 2-50
Conclusion
Homework:
Problems 2-38 to 2-42 and STUDY (or do the next set of HW)
Chapter 1 Individual Test is TOMORROW
Distributive Property
The two methods below multiply two expressions and
rewrite a product into a sum.
Note: There must be two sets of parentheses:
( x – 3 )2 = ( x – 3) ( x – 3 )
FOIL
Box Method
( x + 5 )( x + 3 )
+5 +5x
+15
x
+3x
x2
x
+3
x2 + 8x + 15
•
•
•
•
•
Firsts
( 3x – 2 )( 2x + 7)
Outers
Inners
6x2 + 21x + -4x + -14
Lasts
2 + 17x – 14
=
6x
Simplify
Angles formed by Parallel Lines and a
Transversal
Corresponding - Congruent
b
>
a=b
a
>
100°
100° >
>
Alternate Interior - Congruent
b
a
>
a=b
>
22°
22°
>
>
Same-Side Interior - Supplementary
b
a
>
a + b = 180°
>
60°
120°
>
>
Triangle Angle Sum Theorem
The measures of the angles in a triangle add up to
180°.
mA

mB

mC
180
Example:
B
45°
65°
A
70°
C
2-37: Challenge!
f
g
h
k
m
p
m
57° 123°
h k57°
123°
99°
p 81°
q
g 99°
81°
f
q
r
s
u
v
42°
s
r
81°
57°
v 57°
u
123°
2-43 and 2-44
>
x
y
>
2-43 and 2-44
A
100°
C
B
E
80°
D
2-43 and 2-44
>
112°
68°
>
2-45
80°
>
100°
80°
>
80°100°
80°
>
>
If Same-Side Interior angles are supplementary, then
the lines must be parallel.
If Corresponding angles are congruent, then the lines
must be parallel.
If Alternate Interior angles are congruent, then the
lines must be parallel.
Day 9: February 9th
Objective: Assess Chapter 1 in an individual setting.
• Silence your cell phone and put it in your school bag (not your
pocket)
• Get a ruler, pencil/eraser, and calculator out
• First: Take the test
• Second: Check your work
• Third: Hand the test to Ms. Katz when you’re done
• Fourth: Correct last night’s homework
• Fifth: Work on 2-46/47/48 with your x-value
Homework:
Problems 2-51 to 2-55 AND 2-61 to 2-65
Optional EC: Problem 2-49 neatly done and wellexplained on separate paper to hand-in Monday
Day 10: February 10th
Objective: Find the area of a triangle and develop multiple methods to find
the area of composite shapes formed by rectangles and triangles. THEN
Use rectangles and triangles to develop algorithms to find the area of new
shapes, including parallelograms and trapezoids.
•
•
•
•
•
•
Homework Check and Correct (in red)
Quick Warm-Up
Wrap-Up Problems 2-46 to 2-50
Problems 2-66 to 2-69
Problems 2-75 to 2-79
Conclusion
Homework:
Problems 2-70 to 2-74 and 2-81 to 2-85
Check PowerSchool Sunday night to see if your test grade
has been posted! 
Warm Up! February 10th
Name the relationship between these pairs of angles:
1.
2.
3.
4.
5.
b and d
a and x
d and w
c and w
x and y
b
c
x
w
z
y
a
d
Possible Choices:
Vertical Angles
Straight Angle
Alternate-Interior Angles
Corresponding Angles
Same-side Interior Angles
Area of a Right Triangle
What is the area of the right triangle below?
Why?
4 cm
10 cm
What about non-right triangles?
Height
Height
Where is the Height & Base
Base
Height
Base
Base
Height
Obtuse Triangle
Extra
Base
Area of Obtuse Triangle = Area of Right Triangle
= ½ (Base)(Height)
Area of a Triangle
The area of a triangle is one half the base
times the height.
Base
Base
Height
Height
Height
1
A  bh
2
Base
Can We find the Area?
YES!
YES!
YES!
YES!
YES!
YES!
YES!
YES!
Area of a Parallelogram
Height h
h
h
Base
b
h
Area Rectangle!
= b.h
Area of a Parallelogram
h
b
.
Area = b h
Area of a Parallelogram
The area of a parallelogram is the
base times the height.
.
Area = b h
h
b
20
Ex:
13
5
20
13
A = 20.5 = 100
Area of a Trapezoid
b21
b1
h
Base One
h
Height
b2
h
Base Two
b2
b21
b1
Parallelogram!
Duplicate
Translate
Reflect
Area
= (b1 + b2) h
Area of a Trapezoid
b1
h
b2
1
Area =  b1  b2  h
2
Area of a Trapezoid
The area of a trapezoid is half of the sum of
the bases times the height.
b1
1
Area =  b1  b2  h
2
h
b2
Ex:
9
5
5
4
15
A = ½ (9+15) 4 = ½ . 24 . 4 = 48
Day 11: February 13th
Objective: Explore how to find the height of a triangle given that one side has
been specified as the base. Also, find the areas of composite shapes using
what has been learned about the areas of triangles, parallelograms, and
trapezoids. THEN Review the meaning of square root. Recognize how a
square can help find the length of a hypotenuse of a right triangle.
•
•
•
•
•
•
Homework Check and Correct (in red)
Do Problem 2-79 while you wait for Ms. Katz
Review Chapter 1 Individual Test
Problems 2-86 to 2-89
Problems 2-95 to 2-99
Estimating Square Roots and Simplifying Radicals Lesson
Homework:
Problems 2-90 to 2-94 and 2-100 to 2-104
Optional EC: Problem 2-80 (Separate paper, neat, etc) – Wed.
Team Test Wednesday; Individual Friday (?)
Answers to 2-79
a. 0.5(16)9 = 72 sq. un
b. 26(14) = 364 sq. un
c. 11(11) = 121 sq. un
d. 0.5(6+21)8 = 108 sq. un
Note card = Height Locator
Base
“Weight”
Day 12: February 14th
Objective: Review the meaning of square root. Recognize how a square can
help find the length of a hypotenuse of a right triangle. THEN Learn how to
determine whether or not three given lengths can make a triangle. Also,
understand how to find the maximum and minimum lengths of a third side
given the lengths of the other two sides. THEN Develop and prove the
Pythagorean Theorem.
•
•
•
•
•
Homework Check and Correct (in red)
Finish Problems 2-95 to 2-99
Estimating Square Roots and Simplifying Radicals Lesson
Problems 2-105, 2-106 to 2-108
Start Problems 2-114 to 2-117
Homework:
Problems 2-109 to 2-113 and 2-118 to 2-122
Optional EC: Problem 2-80 (Separate paper, neat, etc) – Wed.
Team Test Tomorrow; Individual Tues/Wed (?)
Triangle Inequality
Each side must be shorter than the sum of
the lengths of the other two sides and longer
than the difference of the other two sides.
b
a–b<c<a+b
a
a–c<b<a+c
c
b–c<a<b+c
Triangle Inequality
Longest Side: Slightly less than the sum of the two
shorter sides
Shortest Side: Slightly more than the difference of the
two shorter sides
Day 13: February 15th
Objective: Develop and prove the Pythagorean
Theorem. THEN Assess Chapter 2 in a team setting.
• Homework Check and Correct (in red)
• Finish Problems 2-114 to 2-117
• Chapter 2 Team Test
Homework: Problems CL2-123 to CL2-131
Chapter 2 Individual Wednesday
The Pythagorean Theorem
a
a
c
b
a
c
c
a
b
2
a +b =c
2
2
b
c
b
c
a
b
2
c
a
c
b
b
c
2
a
a
b
c
a
b
2
Pythagorean Theorem
Leg
B
a
C
2
b
2
2
a +b =c
c
A
Leg
When to use it:
•
If you have a right triangle
•
You need to solve for a side length
•
If two sides lengths are known
Day 14: February 16th
Objective: Learn the concept of similarity and investigate the
characteristics that figures share if they have the same shape.
Determine that two geometric figures must have equal angles to have
the same shape. Additionally, introduce the idea that similar shapes
have proportional corresponding side lengths. THEN Determine that
multiplying (and dividing) lengths of shapes by a common number (zoom
factor) produces a similar shape. Use the equivalent ratios to find
missing lengths in similar figures and learn about congruent shapes.
***NEW SEATS***
• Homework Check and Correct (in red) & Warm-Up!
• Problems 3-2 to 3-5
• Problems 3-10 to 3-15
Homework:
Problems 3-6 to 3-9 AND 3-17 to 3-21
Chapter 2 Individual Wednesday
Dilation
A transformation that shrinks
or stretches a shape
proportionally in all
directions.
Enlarging
3-10
Similar Figures
Exactly same shape but not
necessarily same size
• Angles are congruent
• The ratios between corresponding sides
are equal
21
127°
7
5
127°
90°
15
90°
12
4
53°
90°
10
53°
90°
30
Zoom Factor
The number each side is multiplied
by to enlarge or reduce the figure
x2
x2
Example:
18
3
9
12
x2
24
Zoom Factor = 2
6
Day 15: February 17th
Objective: Examine the ratio of the perimeters of similar figures, and
practice setting up and solving equations to solve proportional problems.
THEN Apply proportional reasoning and learn how to write similarity
statements.
•
•
•
•
Homework Check and Correct (in red) & Warm-Up!
Problems 3-22 to 3-25
Problems 3-32 to 3-37
Conclusion
Homework:
Problems 3-27 to 3-31 AND 3-38 to 3-42
Chapter 2 Individual Wednesday
Warm Up! February 17th
1. If Rob has three straws of different lengths: 4
cm, 9 cm, and 6 cm. Will he be able to make a
triangular picture frame out of the straws?
Why or why not?
2. Find the area of the following shapes:
20 ft
28 ft
40 ft
7 ft
3 ft
10 ft
10 ft
Notation
Angle ABC
Line Segment XY
ABC
XY
mABC
XY
The Measure of
Angle ABC
The Length of
line segment XY
Notation
Acceptable
Not Acceptable
mR  mT
R   T
KT  GB
KT  GB
George Washington’s Nose
720 in
60 ft
in
? ft
? ft
in
ft
? in
Writing a Similarity Statement
Example: ΔDEF~ΔRST
The order of the letters determines which
sides and angles correspond.
B
Z
C
Y
A
ΔABC
ABC ~ ΔZXY
X
Writing a Proportion
B
s
C
W
13
A
25
X
10
D
Z
AB
ABCD
WXYZ
BC ~ WX
XY
WX
AB
=
XY
BC
25
13
=
s
10
Y
Day 16: February 21st
Objective: Learn the SSS~ and AA~ conjectures for determining
triangle similarity. THEN Review Chapter 1 and 2 topics.
•
•
•
•
•
•
Homework Check and Correct (in red) & Warm-Up!
Finish Problem 3-36
Problems 3-43 to 3-47
Review Ch. 2 Team Test (and comments)
Time? Review Ch. 1 and 2 Topics
Conclusion
Homework:
Problems 3-48 to 3-52 AND STUDY!
Chapter 2 Individual Test Tomorrow!
Warm Up! February 21st
Solve the following equations for x:
1.
14
7

x 1 4
2.
3 30  x

2
x
Day 17: February 22nd
Objective: Assess Chapter 2 in an individual setting.
• Silence your cell phone and put it in your school bag (not your
pocket)
• Get a ruler, pencil/eraser, and calculator out
• First: Take the test
• Second: Check your work
• Third: Give test & formula sheet to Ms. Katz when you’re done
• Fourth: Correct last night’s homework
Homework:
Problems 3-59 to 3-63
[We’ll be finishing Ch. 3 this week…tests coming
again soon! ]
Day 18: February 23rd
Objective: Learn how to use flowcharts to organize arguments for
triangle similarity, and continue to practice applying the AA~ and
SSS~ conjectures. THEN Practice making and using flowcharts in
more challenging reasoning contexts. Also, determine the
relationship between two triangles if the common ratio between the
lengths of their corresponding sides is 1.
•
•
•
•
•
Homework Check and Correct (in red)
Problems 3-53 to 3-58
Problems 3-64 to 3-67
Problem 3-73
Conclusion
Homework:
Problems 3-68 to 3-72
First Two Similarity Conjectures
SSS Triangle Similarity (SSS~)
If all three corresponding side lengths share
a common ratio, then the triangles are
similar.
AA Triangle Similarity (AA~)
If two pairs of corresponding angles have
equal measure, then the triangles are
similar.
Similarity and Sides
The following is not acceptable notation:
AB ~ CD
OR
AB  CD
Acceptable:
AB  CD
3-54
T
D
3
C
16
4
2
F
12
Q
8
R
What Conjecture will we use: SSS~
Facts
12
4
3
8
4
2
16
4
4
Conclusion
ΔCDF ~ ΔRTQ SSS~
Another Example
Y
B
100°
100°
A
60°
C
60°
X
Z
What Conjecture will we use: AA~
Facts
mA  mZ
mB  mY
Conclusion
ΔABC ~ ΔZYX AA~
Day 19: February 24th
Objective: Complete the list of triangle similarity conjectures involving sides
and angles, learning about the SAS~ Conjecture in the process. THEN
Practice using the three triangle similarity conjectures and organizing our
reasoning in a flowchart.
•
•
•
•
Homework Check and Correct (in red)
Problems 3-73 to 3-77
Problems 3-83 to 3-86
Conclusion
Homework:
Problems 3-78 to 3-82 AND 3-88 to 3-92
[Optional E.C. – Problem 3-87 neatly and well-done for
Monday]
Chapter 3 Team Test Monday
Chapter 3 Individual Test Wednesday
Conditions for Triangle Similarity
If you are testing for similarity, you can use the
following conjectures:
SSS~
All three corresponding side lengths have
the same zoom factor
AA~
Two pairs of corresponding angles have
equal measures.
14
6
7
3
10
5
55°
40°
40°
55°
SAS~
Two pairs of corresponding lengths have
the same zoom factor and the angles
between the sides have equal measure.
NO CONJECTURE FOR ASS~
40
20
70°
30
70°
15
Day 20: February 27th
Objective: Apply knowledge of similar triangles to multiple contexts. THEN
Assess Chapter 3 in a team setting.
•
•
•
•
•
Homework Check and Correct (in red) & Collect Optional Problem 3-87
Review Chapter 2 Individual Test
Problems 3-93 to 3-95
Chapter 3 Team Test
Conclusion
Homework:
Problems 3-96 to 3-100 and CL3-101 to CL3-110
Chapter 3 Individual Test Wednesday
Day 21: February 28th
Objective: Apply knowledge of similar triangles to multiple contexts. THEN
Review Chapters 1-3 for tomorrow’s individual test.
•
•
•
•
Homework Check and Correct (in red)
Problems 3-93 to 3-95
Review Chapters 1-3
Conclusion
Homework:
Problems 4-6 to 4-10
Chapter 3 Individual Test Tomorrow
Chapter 1-2 Topics
Angles:
• Acute, Obtuse, Right, Straight, Circular – p. 24
• Complementary, Supplementary, Congruent – p. 76
• Vertical, Corresponding, Same-Side Interior, Alternate Interior
– Toolkit and p. 91
Lines:
• Slopes of parallel and perpendicular lines – p. 47
Transformations:
• Reflection, Rotation, Translation, and Prime Notation – p.81
Shapes:
• Name/Define shapes – Toolkit
Probability:
• Use proper notation…Ex: P(choosing a King) = 4/52 = 1/13
– Page 60
Chapter 1-2 Topics
Triangles:
• Triangle Angle Sum Theorem – p.100
• Area
• Triangle Inequality Theorem
Area:
• Triangle, Parallelogram, Rectangle, Trapezoid, Square
– Page 112 and Learning Log/Toolkit
Pythagorean Theorem & Square Roots – p. 115 and 123
Chapter 3 Topics
Dilations
• Zoom Factor – p. 142
Similarity
• Writing similarity statements – p.150
• Triangle Similarity Statements: AA~, SSS~, SAS~
– Page 155 and 171
• Flowcharts
• Congruent Shapes – p. 159
Solving Quadratic Equations – p. 163
You’re Getting Sleepy…
Eye
Height
Eye
Height
x cm
200 cm
Lessons from Abroad
x
316 ft
12 + 930 = 942
6–2=4
12
Day 22: February 29th
Objective: Assess Chapter 3 in an individual setting.
• Silence your cell phone and put it in your school bag (not your
pocket)
• Get a ruler, pencil/eraser, and calculator out
• First: Take the test
• Second: Check your work
• Third: Give test & formula sheet to Ms. Katz when you’re done
• Fourth: Correct last night’s homework
Homework:
Relax! ½ day tomorrow
[and feel extremely fortunate that for ONE night this
semester, you do not have math homework]
Day 23: March 1st
Objective: Recognize that all the slope triangles on a given line are similar to
each other, and begin to connect a specific slope to a specific angle
measurement and ratio.
•
•
•
No HW Check!
Problems 4-1 to 4-5
Conclusion
Homework:
Problems 4-11 to 4-14 [Note: These are classwork problems]
Day 24: March 5th
Objective: Connect specific slope ratios to their related angles and use this
information to find missing sides or angles of right triangles with 11°, 22°, 18°, or
45° angles (and their complements). THEN Use technology to generate slope
ratios for new angles in order to solve for missing side lengths on triangles.
THEN Practice using slope ratios to find the length of a leg of a right triangle and
learn that this ratio is called tangent. Also, practice re-orienting a triangle and
learn new ways to identify which leg is Δx and which is Δy. Learn how to find the
slope ratio using a scientific calculator.
•
•
•
•
•
•
Homework Check and Correct (in red)
Review Problems 4-11 to 4-14
Do Problem 4-15
Problems 4-21 to 4-24
Start Problems 4-30 to 4-35
Conclusion
Homework:
Problems 4-16 to 4-20 AND 4-25 to 4-29
Day 25: March 6th
Objective: Practice using slope ratios to find the length of a leg of a right
triangle and learn that this ratio is called tangent. Also, practice re-orienting
a triangle and learn new ways to identify which leg is Δx and which is Δy.
Learn how to find the slope ratio using a scientific calculator. THEN Apply
knowledge of tangent ratios to find measurements about the classroom.
•
•
•
•
•
•
Homework Check and Correct (in red)
Warm-Up Review Problems
Problems 4-30 to 4-35
Problems 4-41 to 4-42
Review Chapter 3 Individual Test
Conclusion
Homework:
Problems 4-36 to 4-40 AND 4-43 to 4-47
Chapter 4 Team Test Friday
Warm-Up! March 6th
1. The area of the triangle below
is 42 in2. Calculate DC.
2. Simplify:
B
10 in.
A
8 in.
D
C
68 
Warm-Up! March 6th
Solve for x:
x
68°
25 cm
Trigonometry
Theta ( ) is always an acute angle
Opposite
(across from the
known angle)
Δy
h
Hypotenuse
(across from the
90° angle)
Δx
Adjacent
(forms the known angle)
Trigonometry
Theta ( ) is always an acute angle
Opposite
(across from the o
known angle)
h
Hypotenuse
(across from the
90° angle)
a
Adjacent
(forms the known angle)
Trigonometry (LL)
Opposite
Theta ( ) is always an acute angle
h
Adjacent
Trigonometry (LL)
Adjacent
Theta ( ) is always an acute angle
h
Opposite
Day 26: March 7th
Objective: Apply knowledge of tangent ratios to find measurements about the
classroom. THEN Learn how to list outcomes systematically and organize
outcomes in a tree diagram. THEN Continue to use tree diagrams and also
introduce a table to analyze probability problems. Also, investigate the
difference between theoretical and experimental probability.
•
•
•
•
•
•
Homework Check and Correct (in red)
Talk about Tomorrow’s Math Contest (last of the year)
Problem 4-42
Problems 4-48 to 4-53
Problems 4-59 to 4-62
Conclusion
Homework:
Problems 4-54 to 4-58 AND 4-63 to 4-67
Chapter 4 Team Test Friday
When to use Trigonometry
1. You have a right triangle and…
2. You need to solve for a side and…
3. A side and an angle are known
Use Trigonometry
My Tree Diagram
Read
Write
S
T
A
R
T
#41
#28
#55
#81
Listen
Read
Write
Listen
Read
Write
Listen
Read
Write
Listen
One Possibility:
Take Bus #41 and
Listen to an MP3
player
Day 27: March 8th
Objective: Continue to use tree diagrams and also introduce a table to analyze
probability problems. Also, investigate the difference between theoretical and
experimental probability. THEN Learn how to use an area model to represent a
situation of chance. THEN Develop more complex tree diagrams to model
biased probability situations. Further consider the difference between
theoretical and experimental probability.
•
•
•
•
•
Homework Check and Correct (in red)
Finish Problems 4-60 to 4-62
Problems 4-68 to 4-70
Problems 4-77 to 4-80
Conclusion
Homework:
Problems 4-72 to 4-76 AND 4-82 to 4-86
Chapter 4 Team Test Tomorrow
Problem 4-71 is optional extra credit (Get handout from Ms. Katz)
4-60: Tree Diagram
S
T
A
R
T
$100
$300
Keep
$100
Double
$200
Keep
$300
Double
$600
Keep
$1500
Double
$3000
$1500
4-77: Area Diagram
Spinner #2
Spinner #1
T
F
1
3
4
4
I
U
A
1
1
1
2
6
3
IT
UT
AT
1
1
24
1
12
IF
UF
AF
3
3
3
12
8
8
24
Day 28: March 9th
Objective: Assess Chapter 4 in a team setting. THEN Learn about the sine and
cosine ratios. Also, start a Triangle Toolkit.
•
•
•
•
•
Homework Check and Correct (in red)
Chapter 4 Team Test
Problem 4-80 (One more tree diagram to practice)
Start Problems 5-1 to 5-6
Conclusion
Homework:
Problems 4-91 to 4-95 AND CL4-96 to CL4-105
Problem 4-71 is optional extra credit (Get handout from Ms. Katz)
Due Monday
Chapter 4 Individual Test Friday
Day 29: March 12th
Objective: Learn about the sine and cosine ratios. Also, start a Triangle
Toolkit.
•
•
•
•
Homework Check and Correct (in red) & Collect 4-71 (E.C.)
Finish Problems 5-1 to 5-6
Review Chapter 4 Team Test
Conclusion
Homework:
Problems 5-7 to 5-11
Chapter 4 Individual Test Friday
Day 30: March 13th
Objective: Develop strategies to recognize which trigonometric ratio to use
based on the relative position of the reference angle and the given sides
involved.
•
•
•
•
•
•
Homework Check and Correct (in red) & Sign up for Pi Day Snacks
Review Chapter 4 Team Test
Problem 4-80 on Index Card – hand one in as a team for grade
Finish Problem 5-6
Start Problems 5-12 to 5-15
Conclusion
Homework:
Problems 5-16 to 5-20
Bring circular food for tomorrow that you signed up for
Chapter 4 Individual Test Friday
Day 31: March 14th
Objective: Develop strategies to recognize which trigonometric ratio to
use based on the relative position of the reference angle and the
given sides involved.
•
•
•
•
Homework Check and Correct (in red)
Problems 5-12 to 5-15 & Eat Snacks
Clean Up – “Everybody, do your share!”
Conclusion
Homework:
Problems 5-26 to 5-30
Chapter 4 Individual Test Friday
Trigonometry
h
o
a
SohCahToa
opposite
o
sin( ) 

hypotenuse h
adjacent
a
cos( ) 

hypotenuse h
opposite o
tan( ) 

adjacent a
Day 32: March 15th
Objective: Understand how to use trigonometric ratios to find the
unknown angle measures of a right triangle. Also, introduce the
concept of “inverse.” THEN Review for Chapter 4 Individual Test.
THEN Use sine, cosine, and tangent ratios to solve real world
application problems.
•
•
•
•
•
Homework Check and Correct (in red)
Problems 5-21 to 5-25
Ask/Answer any questions from Chapters 1-4
If time, start Problems 5-31 to 5-35
Conclusion
Homework:
Problems 5-36 to 5-40 AND Study like it’s your job!
Chapter 4 Individual Test Tomorrow
Day 33: March 16th
Objective: Assess Chapter 4 in an individual setting.
• Silence your cell phone and put it in your school bag (not your
pocket)
• Get a ruler, pencil/eraser, and calculator out
• First: Take the test
• Second: Check your work
• Third: Give test & formula sheet to Ms. Katz when you’re done
• Fourth: Correct last night’s homework
Homework:
Problems 5-33 to 5-35
[Note: These are classwork problems]
Day 34: March 19th
Objective: Recognize the similarity ratios in 30°-60°-90° and 45°-45°-90°
triangles and begin to apply those ratios as a shortcut to finding
missing side lengths. THEN Learn to recognize 3:4:5 and 5:12:13
triangles, and find other examples of Pythagorean triples. Also,
practice recognizing and applying all three of the new triangle
shortcuts.
•
•
•
•
•
Homework Check and Correct (in red)
Review Problems 5-33 to 5-35
Problems 5-41 to 5-45
Problems 5-51 to 5-55
Conclusion
Homework:
Problems 5-46 to 5-50 AND 5-56 to 5-60
30° – 60° – 90°
A 30° – 60° – 90° is half of an equilateral
(three equal sides) triangle.
30°
s
60°
.5s
s
You can
use this
whenever a
problem
has an
equilateral
triangle!
Long Leg (LL)
30° – 60° – 90°
30°
60°
Short Leg (SL)
30° – 60° – 90°
Remember
√3 because
there are 3
different
angles
You MUST
know SL first!
√3
30°
2
÷2
60°
1
÷√3
SL
LL
x√3
x2
Hyp
Isosceles Right Triangle
45° – 45° – 90°
Remember
√2 because 2
angles are
the same
45°
√2
1
45°
÷√2
Leg(s)
1
Hypotenuse
x√2
Isosceles Right Triangle
45° – 45° – 90°
A 45° – 45° – 90° triangle is half of a square.
45°
s
d
45°
s
You can
use this
whenever a
problem
has a
square with
its diagonal!
Day 35: March 20th
Objective: Learn to recognize 3:4:5 and 5:12:13 triangles, and find other
examples of Pythagorean triples. Also, practice recognizing and
applying all three of the new triangle shortcuts. THEN Review tools
for finding missing sides and angles of triangles, and develop a
method to solve for missing sides and angles for a non-right triangle.
•
•
•
•
Homework Check and Correct (in red)
Problems 5-51 to 5-55
Problems 5-61 to 5-65
Conclusion
Homework:
Problems 5-67 to 5-72
Pythagorean Triple
A Pythagorean triple consists of three positive
integers a, b, and c (where c is the greatest)
such that:
a2 + b2 = c 2
Common examples are:
3, 4, 5 ; 5, 12, 13 ; and 7, 24, 25
Multiples of those examples work too:
3, 4, 5 ; 6, 8, 10 ; and 9, 12, 15
Day 36: March 21st
Objective: Review tools for finding missing sides and angles of triangles,
and develop a method to solve for missing sides and angles for a
non-right triangle. THEN Recognize the relationship between a side
and the angle opposite that side in a triangle. Also, develop the Law
of Sines and use it to find missing side lengths and angles of nonright triangles. THEN Complete the Triangle Toolkit by developing the
Law of Cosines.
•
•
•
•
•
Homework Check and Correct (in red)
Finish Problems 5-61 to 5-65
Problems 5-73 to 5-76
Start Problems 5-85 to 5-88
Conclusion
Homework:
Problems 5-79 to 5-84 AND 5-89 to 5-94
Ch. 5 Team Test Soon?
Day 37: March 22nd
Objective: Review and practice using the Law of Sines. THEN
Complete the Triangle Toolkit by developing the Law of Cosines.
•
•
•
•
•
•
Homework Check and Correct (in red)
Summarize Law of Sines in Angle Toolkit
Practice WS - #1,2,6,7 on Law of Sines
Problems 5-85 to 5-88
Practice Law of Cosines if time
Conclusion
Homework:
Problems 5-100 to 5-105
Ch. 5 Team Test Tomorrow
Midterm (Ch. 5 Individual Test) Next Friday
Day 38: March 23rd
Objective: Complete the Triangle Toolkit by developing the Law of
Cosines. THEN Assess Chapter 5 in a team setting.
•
•
•
•
•
Homework Check and Correct (in red)
Practice Law of Sines and Cosines
Chapter 5 Team Test
Problem 5-95 and Discussion
Conclusion
Homework:
Problems 5-114 to 5-125 Double set!
Midterm (Ch. 5 Individual Test) Next Friday
Day 39: March 26th
Objective: Learn that multiple triangles are sometimes possible when
two side lengths and an angle not between them are given (SSA).
THEN Apply current triangle tools to solve multiple problems and
applications.
•
•
•
•
•
Homework Check and Correct (in red)
Problem 5-95 and Discussion
Problems 5-106 to 5-113
Review Chapter 5 Team Test
Conclusion
Homework:
Problems CL5-126 to CL5-136
Midterm (Ch. 5 Individual Test) Friday
[If you know you’re not going to be here due to
extenuating circumstances, you must see me ahead of
time to take the exam.]
Day 40: March 27th
Objective: Practice identifying congruent triangles by first determining
that the triangles are similar and that the ratio of corresponding sides
is 1. THEN Use our understanding of similarity and congruence to
develop triangle congruence shortcuts.
•
•
•
•
Homework Check and Correct (in red)
Problems 6-1 to 6-3
Problems 6-10 to 6-12
Conclusion
Homework:
Problems 6-4 to 6-9 AND 6-13 to 6-18
Midterm (Ch. 5 Individual Test) Friday
[If you know you’re not going to be here due to
extenuating circumstances, you must see me ahead of
time to take the exam.]
Conditions for Triangle Similarity
If you are testing for similarity, you can use the
following conjectures:
SSS~
All three corresponding side lengths have
the same zoom factor
7
3
10
5
AA~
Two pairs of corresponding angles have
equal measures.
55°
55°
40
20
70°
NO CONJECTURE FOR ASS~
40°
40°
SAS~
Two pairs of corresponding lengths have
the same zoom factor and the angles
between the sides have equal measure.
14
6
30
70°
15
Conditions for Triangle Congruence
If you are testing for congruence, you can use the following conjectures:
5
SSS 
All three pairs of corresponding side
lengths have equal length.
3
SAS 
Two pairs of corresponding sides have
equal lengths and the angles between
the sides have equal measure.
7
3
5
ASA 
Two angles and the side between them
are congruent to the corresponding
angles and side lengths.
7
40°
10
55°
10
55°
40°
20
20
70°
70°
15
15
Conditions for Triangle Congruence
If you are testing for congruence, you can use the following conjectures:
AAS 
Two pairs of corresponding angles and
one pair of corresponding sides that
are not between them have equal
measure.
51
51 42°
42°
44°
44°
HL 
The hypotenuse and a leg of one right
triangle have the same lengths as the
hypotenuse and a leg of another right
triangle.
NO CONJECTURE FOR ASS 
19
23
23
19
Day 41: March 28th
Objective: Extend the use of flowcharts to document triangle congruence
facts. Practice identifying pairs of congruent triangles and contrast
congruence arguments with similarity arguments. THEN Recognize the
converse relationship between conditional statements, and then
investigate the relationship between the truth of a statement and the truth
of its converse.
•
•
•
•
Homework Check and Correct (in red)
Finish Problem 6-12
Problems 6-19 to 6-23
Problems 6-30 to 6-33
Homework:
Problems 6-24 to 6-29 AND 6-35 to 6-40
Chapter 6 Team Quiz Tomorrow (?)
Midterm (Ch. 5 Individual Test) Friday
[If you know you’re not going to be here due to extenuating
circumstances, you must see me ahead of time to take the exam.]
Problem 6-12
Complete 6-12 on page 295:
Use your triangle congruence conjectures to
determine if the following pairs of triangles
must be congruent.
SAS
SAS
SSS
ASS
ASA
AAS
Problem 6-12 Continued
Complete 6-12 on page 295:
Use your triangle congruence conjectures to
determine if the following pairs of triangles
must be congruent.
SSS
AAS
ASS
AAA
Example 1
Determine if the triangles below are congruent. If the
triangles are congruent, make a flowchart to justify
your answer.
A
B
C
D
Example 2
Determine if the triangles below are congruent. If the
triangles are congruent, make a flowchart to justify
your answer.
A
C
>
>
E
B
D
Day 42: March 29th
Objective: Assess Chapter 6 in a team setting. THEN
Review Chapters 1-5 as needed.
• Homework Check and Correct (in red)
• Chapter 6 Team Quiz
• Review/Ask Questions for Midterm
Homework: Problems 6-43 to 6-48
Midterm (Ch. 5 Individual Test) Tomorrow!
Day 43: March 30th
Objective: Assess Chapters 1-5 in an individual setting.
• Silence your cell phone and put it in your school bag (not your
pocket)
• Get a ruler, pencil/eraser, and calculator out
• First: Take the test
• Second: Check your work
• Third: Give exam & formula sheet to Ms. Katz when you’re done
• Fourth: Correct last night’s homework
Homework: Problems 6-61 to 6-66
Bring your Geometry textbook from home on Tuesday!!!
Enjoy your week away from school!
Day 44: April 10th
Objective: Review recent assessments. THEN Review for
Chapter 6 individual test.
*Beginning of Quarter 4*
• Homework Check and Correct (in red)
• Trade Textbooks
• Review Midterm (With example slides and OSCAR data)
• Review Chapter 6 Team Quiz
• Do Chapter 6 Closure
Homework:
Problems 7Chapter 6 Individual Test Friday