Transcript Honors Geometry Volume 1 Spring 2016x

Honors Geometry
Spring 2016
Mrs. Poppiti
Day 1: February
st
1
Objective: Form and meet study teams. THEN Build the biggest box possible
from a single sheet of paper; decide how we will determine which box is
the “biggest”. THEN Build an understanding of area and perimeter.
Investigate how the perimeter and area of a shape change as the shape is
enlarged proportionally.
 Seats and Fill out Index Card (questions on next slide)
 Introduction: Mrs. Poppiti, Books, Syllabus, Homework Record,
Expectations
 Quick Pairs Introduction
 Activity: Building the Biggest
 Problems 1-19 and 1-24
Homework:
Do Problems 1-3 to 1-7 AND 1-14 to 1-18;
Supplies (Monday at the latest); Have parent/
guardian fill out last page of syllabus and sign;
Extra credit tissues or lysol wipes
Respond on Index Card:
1. When did you take Algebra 1?
2. Who was your Algebra 1 teacher?
3. What grade do you think you earned in Algebra 1?
4. What is one concept/topic from Algebra 1 that Ms. Poppiti could
help you learn better?
5. What grade would you like to earn in Geometry?
(Be realistic)
6. What sports/clubs/activities/jobs are you involved in this Spring?
7. E-mail address that you check regularly – PRINT CLEARLY!
Support
 www.cpm.org
 Resources (including worksheets from class)
 Extra Support/Practice
 Parent Guide
 Free Homework Help
 Mrs. Poppiti’s webpage on the HHS website
 Classwork and Homework Assignments
 Worksheets
 Extra Resources
Building the Biggest
 Your main task in this activity is to build the biggest box you
can from a single sheet of construction paper. In this activity,
“biggest” means “holding the most” and “box” means a
container with four rectangular sides, a rectangular bottom, and
no top.
 You can cut your construction paper and tape pieces together in
any way you want as long as your final product is a box. If your
first attempt does not satisfy you, try again. Keep working at it
until you think you have built the biggest box possible.
 Once you have a container that you are satisfied with, it is time
to test its capacity! Fill your paper container with puffed rice,
and compare with other teams’ containers. Your teacher will
instruct you as to how to make the comparison/measurement.
The “winning” container will be the one that holds the largest
amount of puffed rice.
Day 2: February
nd
2
Objective: Build an understanding of area and perimeter. Investigate how
the perimeter and area of a shape change as the shape is enlarged
proportionally. THEN Build an understanding of what an angle is and
how it is measured. Introduce complicated shapes composed of triangles,
and begin to use attributes of sides and angles to compare and describe
those shapes. THEN Use spatial visualization skills to investigate
reflection.




HW Check/Correct in RED
Finish Problems 1-19 and 1-24
Problems 1-37 to 1-40
Start Problems 1-47 to 1-52
Homework:
Do Problems 1-25 to 1-29 AND 1-32 to 1-36;
Supplies (Monday at the latest); Have parent/
guardian fill out last page of syllabus and sign;
Extra credit tissues or lysol wipes
Carpetmart
• What is perimeter?
• What does perimeter measure?
• What are the units used to measure area?
• Why are they different from the units used to measure
length?
• See Math Notes Box on Perimeter and Area
• Look for patterns!
• Help each other – everyone has strengths and weaknesses!
Types of Angle Measures (pg 24)
Acute: Between 0° and 90°
Right: 90°
Straight: 180°
Obtuse: Between 90° and 180°
Circular: 360°
Day 3: February
rd
3
Objective: Use 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. THEN 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).





HW Check/Correct in RED & Comlete Warm-Ups (on white board)
LL Notes: “Complete Graph” – for HW tonight (and in the future)
Finish Problems 1-50 to 1-52
Problems 1-59 to 1-62
Start Problems 1-69 to 1-72
Homework:
Do Problems 1-42 to 1-46 AND 1-54 to 1-58;
Get Supplies! (Supplies check Monday)
Ch. 1 Team Test Monday? Individual Test Wed?
Complete Graph
When a problem says graph an equation or draw a graph:
y
On graph paper:
Plot key points
accurately
Use a ruler!
(-2,0)
(3,0)
x
Scale your axes
appropriately
(0,-6)
(.5,-6.25)
Label the axes
(with units if
appropriate)
Day 4: February
th
4
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.




HW Check/Correct in RED & Complete Warm-Ups (on white board)
LL Notes
Problems 1-69 to 1-72
Problems 1-87 to 1-91
Homework:
Do Problems 1-63 to 1-67 AND 1-73 to 1-77;
Get Supplies! (Supplies check Monday)
Ch. 1 Team Test Monday? Individual Test Wed?
Prime Notation (pg 34)
When labeling a transformation, the new figure (called
the image) is labeled with prime notation.
– Example: If ΔABC is reflected across the vertical dashed line,
its image can be labeled ΔA’B’C’ to show exactly how the new
points correspond to the points in the original shape.
B’
B
C
A
C’
A’
Rigid Transformations (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
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.
yintercept
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
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. You look in a mirror as you comb your hair.
B. While repairing your bicycle, you turn it upside down and spin
the front tire to make sure it isn’t rubbing against the frame.
C. You move a small statue from one end of a shelf to the other.
D. You flip your scrumptious buckwheat pancakes as you cook
them on the griddle.
E. The bus tire spins as the bus moves down the road.
F. You examine footprints made in the sand as you walked on the
beach.
Reflection across a side
The two shapes MUST meet at a side that
has the same length.
1-71: Reflections
1. Lines that connect corresponding points
perpendicular
are _____________
to the line of
reflection.
bisects each of the
2. The line of reflection ______
segments connecting a point and its image.
Day 5: February
th
5
Objective: Learn about reflection, rotation, and translation symmetry.
Identify which common shapes have each type of symmetry. THEN 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.





HW Check/Correct in RED & Complete Warm-Up (on white board)
Explain Math Contest…
Block 2: Finish Problems 1-71 to 1-72
Problems 1-87 to 1-91
Problems 1-97 to 1-98 AND 1-104
Homework:
Do Problems 1-82 to 1-86 AND 1-92 to 1-96;
Get Supplies! (Check on Monday) Extra Credit?
Ch. 1 Team Test Tuesday
Ch. 1 Individual Test Thursday
1-72
B
A
A’
Isosceles Triangle
Sides: two sides
of equal length
Base Angles:
Have the same
measure
Height: Perpendicular
to the base AND splits
the base in half
Day 6: February
th
8
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.





HW Check/Correct in RED & Complete Warm-Up (board & next slide)
Supplies Check!
Block 2: Finish Rotational Symmetry talk + Translation + Notes
Problems 1-97 to 1-98
Problems 1-104 to 1-108
Homework:
Do Problems 1-99 to 1-103 AND 1-110 to 1-114
Math Contest Tomorrow!
Ch. 1 Team Test Tomorrow
Ch. 1 Individual Test Thursday
Day 6: Try This!
Rotate Figure D 90° about the origin into each of the other 3 quadrants.
Note any patterns that you see in the coordinates of the transformed
images.
 6, 3
 7, 8
1.87-88
6 Ref.
60 rot.
0 Ref. No Rot.
1 Ref.
No rot.
3 Ref. 120 Rot
2 Ref.
0 Ref.
180 rot.
No rot.
4 Ref. 90 rot.
1 Ref. No rot.
1.87-88
2 Ref. 180 Rot
Inf. Ref. Inf. Rot
0 Ref. No Rot
1 Ref. No Rot
0 Ref. No Rot
1 Ref. No Rot
5 Ref. 72 Rot
0 Ref. 180 Rot
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)
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
1.98 a
1. Has at least 1 pair of
Parallel sides
2. Has at least 2 sides of
equal length
1.98 b
1. Has only 3 sides
2. Has a right angle
1.98 c
1. Has reflection symmetry
2. Has 180 rotation
symmetry
1.104
1. Quadrilateral
2. Equilateral
Describing a Shape
Day 7: February
th
9
Objective: Assess Chapter 1 in a team setting. 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.
 HW Check/Correct in RED & Complete Warm-Up (on the
board)
 Chapter 1 Team Test (≤ 50 minutes)
 Finish Problems 1-107 to 1-108
Homework:
Problems 1-121 to 1-129 AND Review Worksheet
Ch. 1 Individual Test Thursday
Day 7: Try This!
Algebraically, solve for x:
1 2x 1 x  5 1



1
2
3
3
3
6
x 5
2x 1 
6
6  2 x  1  x  5
12 x  6  x  5
6
12 x  6  x  5
11x  6  5
11x  11
x  1
Shape Toolkit
Shape Toolkit
Day 8: February
th
10
Objective: Develop an intuitive understanding of probability, and
apply simple probability using the shapes in the Shape Bucket.
 HW Check/Correct in RED
 Review Chapter 1 Team Test
 Problem 1-108
 Problems 1-115 to 1-119
 Extra Review (Practice) – 6 Questions on Slides
Homework:
Problems CL1-130 to CL1-134 & STUDY!!!
Ch. 1 Individual Test Tomorrow
Day 8: Try This!
1. Solve the following equation for x:




2
1
3 x  x  7 3
3
5
3
5 2 x  x  21 5
5
10 x  3 x  105
7 x  105
x  15
2. Rotate the point (-6, 2) 90 degrees clockwise about
the point (-1, 4). Where is the image located?
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
Question 0
1. The area of the following rectangle is 2 x 2  54.
Write an equation involving all of the information given.
x 3
Solve your equation.
2x
2
2. Find the equation of the line perpendicular to y  x  5
7
that passes through the point  2, 7  .
Show the algebraic process.
Question 1
If the length of a rectangle is 5 less than 4 times the width, and the
perimeter is 40 inches, what is the area of the rectangle?
[A] 15 in2
[B] 75 in2
[C] 30 in2
[D] 5 in2
Question 2
Solve for x:
[A] x = -4
[B] x = -3
[C]
x = 10 [D] x = 3
Question 3
Which of the following represents the system below?
Question 4
If the point (6, -3) is rotated 270 degrees clockwise about the origin, where
would the new image be located?
[A] (3, -6)
[B] (-6, -3)
[C] (-3, -6)
[D] (3, 6)
Day 9: February
th
11
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 & formula sheet to Mrs. Poppiti when
finished
• Fourth: Check last night’s homework
• If time remains, we’ll start Chapter 2 together!
Homework: Problems 2-8 to 2-12
Day 10: February
th
12
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.
 HW Check/Correct in RED
 Problems 2-1 to 2-7
 Circle Activity (10 minutes)
Homework:
Finish Problems 2-2 to 2-6 AND Do 2-18 to 2-22
2-2
A
C’
a.
B
B’
C
b.
c.
6
Day 11: February
th
16
Objective: 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. THEN
Continue to apply knowledge of corresponding angles, and
develop conjectures about alternate interior and same-side
interior angles. Also, learn about how light reflects off a mirror.
 HW Check/Correct in RED
 Review Problems 2-4 to 2-7 as necessary
 LL Notes: Notation for Angles & Angle Types
 Problems 2-13 to 2-17
 Start Problems 2-23 to 2-28
Homework:
Problems 2-29 to 2-33
Notation for Angles
F
E
D
Name
or
Measure
Correct:
If there is only one angle at the
vertex, you can also name the
angle using the vertex:
Y
W
X
Z
?
Incorrect:
?
Incorrect:
Angle Types (pg 76)
Complementary Angles: Two angles
that have measures that add up
to 90°.
30°
60°
x°
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.
Day 12: February
th
17
Objective: Continue to apply knowledge of corresponding angles,
and develop conjectures about alternate interior and same-side
interior angles. Also, learn about how light reflects off a mirror.
THEN Discover the triangle angle sum theorem, and practice
finding angles in complex diagrams that use multiple
relationships.
 HW Check/Correct in RED
 Finish Problems 2-15 to 2-17
 Problems 2-23 to 2-28
 Start Problems 2-34 to 2-37
Homework:
Problems 2-38 to 2-42
2-16
X
X
Why Parallel Lines?
53°
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)
Angles formed by parallel lines and a
transversal
Corresponding - Congruent
b
a
>
>
>
100°
a=b
Alternate Interior - Congruent
b
a
>
>
a=b
100° >
22°
22°
>
>
Same-Side Interior - Supplementary
b
a
>
>
a + b = 180°
60°
120°
>
>
Day 13: February
th
18
Objective: Discover the triangle angle sum theorem, and practice
finding angles in complex diagrams that use multiple
relationships. THEN Learn the converses of some angle
conjectures. Also, apply knowledge of angle relationships to
analyze the hinged mirror trick from Lesson 2.1.1.
 HW Check/Correct in RED & Complete Warm-Up (Next Slide)
 Problems 2-34 to 2-37
 Problems 2-43 to 2-50
Homework:
Problems 2-51 to 2-55 AND 2-61 to 2-65
Day 13: Try This!
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
a
d
Possible Choices:
w x
z y
Vertical Angles
Straight Angle
Alternate-Interior Angles
Corresponding Angles
Same-side Interior Angles
Triangle Angle Sum Theorem
The measures of the angles in a triangle add up to
180°.
Example:
B
45°
A
65°
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 14: February
th
19
Objective: Learn how to 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.
 HW Check/Correct in RED & Complete Warm-Up (Handout)
 Review Chapter 1 Individual Test
 Problems 2-66 to 2-68
 Problems 2-75 to 2-79
Homework:
Problems 2-70 to 2-74 AND …?
Area of a 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?
Height
Base
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!
Day 15: February
nd
22
Objective: Use rectangles and triangles to develop algorithms to
find the area of new shapes, including parallelograms and
trapezoids. THEN 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.
 HW Check/Correct in RED & Complete Warm-Up (Handout)
 Finish Problems 2-75 to 2-79
 Problems 2-86 to 2-89
Homework:
Problems 2-81 to 2-85 AND 2-90 to 2-94
Area of a Parallelogram
h
h
Height
Base
b
h
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
b2
h
b21
Base Two
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
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
Notecard = Height Locator
Base
“Weight”
Day 16: February
rd
23
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.
 HW Check/Correct in RED
 FIX 2-88 and Finish!
 Problems 2-95 to 2-99
 Problems 2-105 to 2-108
Homework:
Problems 2-100 to 2-104 AND 2-109 to 2-113
Ch. 2 Team Test Tomorrow
Ch. 2 Individual Test Friday
Triangle Inequality Theorem
Longest Side: Slightly less than the sum of the two
shorter sides
Shortest Side: Slightly more than the difference of the
two longer sides
Triangle Inequality Theorem
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
c
|a – b| < c < a + b
|a – c| < b < a + c
|b – c|< a < b + c
Day 17: February
th
24
Objective: Develop and prove the Pythagorean Theorem. THEN
Assess Chapter 2 in a team setting.
 HW Check/Correct in RED
 Problems 2-114 to 2-117
 If time: Mini Review Lesson on Simplifying Radicals
 Chapter 2 Team Test
Homework:
Problems 2-118 to 2-122 AND Review WS
Ch. 2 Individual Test Friday
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 side lengths are known
Day 18: February
th
25
Objective: Review concepts from Chapters 1-2 in preparation for
the individual test.
 HW Check/Correct in RED
 Review Chapter 2 Team Test
 Mini Lesson/Review: Simplifying Radicals + Practice
 Calculate EXACT perimeters of shapes in Problem 2-90
 Pythagorean Theorem slide (tough type)
 Extra Practice Options: Areas, Mixed Review, etc?
Homework:
Problems CL2-123 to CL2-131 AND STUDY!!!!!!
Don’t know how to study? See me for ideas!
Ch. 2 Individual Test Tomorrow
Pythagorean Theorem Example
Solve for the length of the missing side:
3 2
a 2  b2  c2
x
6 5
3 2 
2

x  6 5
2

2
18  x 2  180
x 2  162
x  162
x  81 2
x  9 2 un.
Day 19: February
th
26
Objective: Assess Chapters 1-2 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: Hand the test & formula sheet to Mrs. Poppiti when
finished
• Fourth: Check last night’s homework
• If time remains, we’ll start Chapter 3 together!
Homework: Worksheet – Pythagorean Theorem & Its Converse
Day 20: February
th
29
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.
CIRCLE THEN *** NEW SEATS ***
 HW Check/Correct in RED
 Problems 3-1 to 3-5
 Problems 3-10 to 3-14
Homework:
Problems 3-6 to 3-9 AND 3-17 to 3-21
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
• Corresponding 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
Day 21: March
st
1
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.
 HW Check/Correct in RED & Complete Warm-Up (Next Slide)
 Check/Review Problems 3-10 to 3-14
 Problems 3-22 to 3-26
 Problems 3-32 to 3-37
 Review Chapter 2 Individual Test
Homework:
Problems 3-27 to 3-31 AND 3-38 to 3-42
Day 21: Try This!
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
10 ft
3 ft
10 ft
Zoom Factor
The number each side is multiplied
by to enlarge or reduce the figure
x2
x2
Example:
18
4
9
12
x2
24
Zoom Factor = 2
8
George Washington’s Nose
720 in
60 ft
in
? ft
? ft
in
ft
? in
Day 22: March
nd
2
Objective: Apply proportional reasoning and learn how to write
similarity statements. THEN Learn the SSS~ and AA~ conjectures
for determining triangle similarity. THEN Learn how to use
flowcharts to organize arguments for triangle similarity, and
continue to practice applying the AA~ and SSS~ conjectures.
 HW Check/Correct in RED & Finish 3-34 to 3-37
 Check/Review Problems 3-34 to 3-37
 LL Notes to summarize
 Problems 3-43 to 3-47
 Start Problems 3-53 to 3-58
Homework:
Problems 3-48 to 3-52 & Radicals WS 1-11 ODDS
Chapter 3 Team Test Tuesday
Chapter 3 Individual Test Thursday
Notation
Angle ABC
Line Segment XY
The Measure of
Angle ABC
The Length of
line segment XY
Notation
Acceptable
KT  GB
Not Acceptable
KT  GB
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 ~ ΔZ XY
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
First Two Similarity Conjectures
SSS Triangle Similarity (SSS~)
If all three pairs of 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.
Day 23: March
rd
3
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.
x
3
=
 HW Check/Correct in RED & Solve:
4 x +1
 Problems 3-53 to 3-58
 Problems 3-64 to 3-67
Homework:
Problems 3-59 to 3-63 & 3-68 to 3-72
Chapter 3 Team Test Tuesday
Chapter 3 Individual Test Thursday
3-54
T
D
3
C
16
4
2
F
12
Q
8
R
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B  mY
mA  mZ
Conclusion
ΔABC ~ ΔZYX
AA~
Similarity and Sides
The following is not acceptable notation:
AB ~ CD
OR
AB  CD
Acceptable:
AB  CD
OR
AB  CD
Day 24: March
th
4
Objective: 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. THEN Complete the list of triangle
similarity conjectures involving sides and angles, learning about the
SAS~ Conjecture in the process.
 HW Check/Correct in RED QUICKLY!
 Finish Problems 3-65 to 3-67
 Problems 3-73 to 3-77
Homework:
Problems 3-78 to 3-82;
Finish ODDS on Add/Subtract Radicals WS
Chapter 3 Team Test Tuesday
Chapter 3 Individual Test Thursday
Day 25: March
th
7
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 reasoning in a flowchart.
 HW Check/Correct in RED QUICKLY & Complete Warm-Ups
 Problems 3-73 to 3-77
 Problems 3-83 to 3-86
Homework:
Problems 3-88 to 3-92 AND
Pages 1-2 in Ch. 3 Review Packet
Chapter 3 Team Test Tomorrow
Chapter 3 Individual Test Thursday
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.
70°
NO CONJECTURE FOR ASS~
3
0
40
20
70°
15
Day 26: March
th
8
Objective: Assess Chapter 3 in a team setting. THEN Apply
knowledge of similar triangles to multiple contexts.
 HW Check/Correct in RED QUICKLY & Complete Warm-Up
 Chapter 3 Team Test
 Problems 3-94 to 3-95
Homework:
Problems 3-96 to 3-100 AND
Finish Ch. 3 Review Packet
Chapter 3 Individual Test Thursday
Day 27: March
th
9
Objective: Apply knowledge of similar triangles to multiple contexts.
THEN Review concepts in preparation for tomorrow’s assessment.
 HW Check/Correct in RED QUICKLY & Complete Warm-Ups
 Review Chapter 3 Team Test
 Tough Trapezoids Practice
 Hallway Relay
 Problems 3-94 to 3-95
 Carousel Cards: Proof/Flowchart Practice?
Homework:
Problems CL3-102 to 3-110 (Skip 106)
Chapter 3 Individual Test Tomorrow – STUDY!!!
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 28: March
th
10
Objective: Assess Chapters 1-3 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: Hand the test & formula sheet to Mrs. Poppiti when
finished
• Fourth: Check last night’s homework
Homework: Problems 4-6 to 4-10
Day 29: March
th
11
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. THEN 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).
***BRIEF CIRCLE***
 HW Check/Correct in RED
 Problems 4-1 to 4-5
 Problems 4-11 to 4-15
Homework:
Problems 4-16 to 4-20 AND 4-25 to 4-29
Day 30: March
th
14
Objective: 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.
***BRIEF CIRCLE***
 HW Check/Correct in RED & Warm-Up (Next Slide)
 Lesson 4.1.3: Problems 4-21 to 4-24
 Problems 4-30 to 4-35
Homework:
Problems 4-36 to 4-40 AND Tangent Worksheet
Try This!
Solve for x:
x
68°
25 un
Day 31: March
th
15
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 reorienting 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. THEN Learn how to list
outcomes systematically and organize outcomes in a tree diagram.
 HW Check/Correct in RED
 Finish Problems 4-33 to 4-35, 4-36
 Problems 4-41 to 4-42
 Problems 4-48 to 4-53
Homework:
Problems 4-43 to 4-47 AND 4-54 to 4-58
AND Front side of Tangent Worksheet
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 (LL)
Opposite
Theta ( ) is always an acute angle
h
Adjacent
Trigonometry (LL)
Adjacent
Theta ( ) is always an acute angle
h
Opposite
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 acute angle are known
Use Trigonometry
Day 32: March
th
16
Objective: 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. THEN Learn how to use an area model (and a generic
area model) to represent a situation of chance.
 HW Check/Correct in RED
 Review Ch. 3 Individual Test
 Finish Problems 4-50 to 4-53
 Problems 4-59 to 4-62
 Start Problems 4-68 to 4-70
Homework:
Problems 4-63 to 4-67 AND 4-72 to 4-76
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
4-60: Tree Diagram
S
T
A
R
T
$100
$300
Keep
$100
Double
$200
Keep
$300
Double
$600
Keep
$1500
Double
$3000
$1500
Day 33: March
th
17
Objective: Learn how to use an area model (and a generic area model)
to represent a situation of chance.
 HW Check/Correct in RED
 Warm-Up – Complete individually and hand-in when done
 Problems 4-68 to 4-70
 Problems 4-77 to 4-81
Homework:
Problems 4-82 to 4-86 AND 4-91 to 4-95
4-77: Area Model
Spinner #1
Spinner #2
I
T
F
U
A
1
 2
1
 6
 3
 4
IT
UT
AT
1
1
24
1
12
 4
IF
UF
AF
3
3
3
12
1
3
8
8
24
1
Day 34: March
th
18
Objective: Learn how to use an area model (and a generic area model)
to represent a situation of chance. THEN Learn about the sine and
cosine ratios. Also, start a Triangle Toolkit.
 HW Check/Correct in RED & Calculate EXACT area and
perimeter for each shape drawn on the board
 Problem 4-80
 Problems 5-1 to 5-6
Homework:
Chapter 4 Review Sheet
Optional: Extra study items (2 packets)
Chapter 4 Team Test Wednesday
Chapter 4 Individual Test Friday
Day 35: March
th
29
Objective: Learn about the sine and cosine ratios. Also, start a Triangle
Toolkit. THEN Develop strategies to recognize which trigonometric
ratio to use based on the relative position of the reference angle and
the given sides involved.
 HW Check/Correct in RED
 Answer questions from Chapter 4 Review efforts
 Problem 5-6 (Toolkit Entry)
 Problems 5-12 to 5-15
Homework:
Problems 5-7 to 5-12 AND 5-16 to 5-20
Chapter 4 Team Test Wednesday
Chapter 4 Individual Test Friday
Day 36: March
th
30
Objective: Assess Chapter 4 in a team setting. THEN Understand how
to use trigonometric ratios to find the unknown angle measures of a
right triangle. Also, introduce the concept of “inverse.”
 HW Check/Correct in RED
 Chapter 4 Team Test
 Problems 5-21 to 5-25
Homework:
Problems 5-26 to 5-30
Chapter 4 Individual Test Friday
Chapter 5 Team Test Next Thursday (?)
Day 37: March
st
31
Objective: Understand how to use trigonometric ratios to find the
unknown angle measures of a right triangle. Also, introduce the
concept of “inverse.” THEN Use sine, cosine, and tangent ratios to
solve real world application problems.
 HW Check/Correct in RED
 Review Chapter 4 Team Test
 Problems 5-21 to 5-25
 Problems 5-31 to 5-35
Homework:
Problems 5-36 to 5-40 AND STUDY!
Chapter 4 Individual Test Tomorrow
Chapter 5 Team Test Next Thursday (?)
Day 38: April
st
1
Objective: Assess Chapters 1-4 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: Hand the test & formula sheet to Mrs. Poppiti when
finished
• Fourth: Check last night’s homework
Homework:
Problems 5-33(c) to 5-35 AND Trig/Inv Trig WS
Chapter 5 Team Test Next Thursday (?)
Ch. 5 Individual Test IS the midterm…
Day 39: April
th
4
Objective: Use sine, cosine, and tangent ratios to solve real world
application problems. THEN 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.
NEW SEATS!!






HW Check/Correct in RED & Complete Warm-Ups (On Board)
Review Problems 5-33 to 5-35
LL Entry: Trig Memory Tool
Review Ch. 4 Individual Test
Problems 5-41 to 5-44
Notes (Toolkit and Learning Log Entries)
Homework:
Problems 5-46 to 5-50
Chapter 5 Team Test Thursday (?)
Trigonometry
h
o
a
SohCahToa
opposite
o
sin( ) 

hypotenuse h
adjacent
a
cos( ) 

hypotenuse h
opposite o
tan( ) 

adjacent a
30° - 60° - 90°
A 30° – 60° – 90° is half of an equilateral
(three equal sides) triangle.
30°
s
60°
0.5s
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
1
÷√3
SL
LL
x√3
x2
Hyp
2
60°
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
You can use
this whenever
a problem has
a square with
its diagonal!
d
45°
s
Pythagorean Triple
A Pythagorean triple consists of three positive
integers a, b, and c (where c is the greatest) such that:
a2 + b2 = c2
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