Honors Geometry

Spring 2012Ms. 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)

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. 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:

Respond on Index Card:

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

Cut along dotted line

Write sentence and names around the gap.

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

• Use the equation to find y-values

• Complete the graph by scaling and labeling the axes

• Graph and connect the points from your table. Then label the line.

x -4 -3 -2 -1 0 1 2 3 4y 13 11 9 7 5 3 1 -1 -3

-5-10 105

y = -2x+5

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)

Reflection: Mirror image over a line

Rotation: Turning about a point clockwise or counter clockwise

Translation: Slide in a direction

Transformation: A movement that preserves size and shape

Everyday Life SituationsHere are some situations that occur in everyday life. Each oneinvolves 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.

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

SymmetrySymmetry: 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)

Isosceles Triangle

Sides: AT LEAST two sides of equal length

Height: Perpendicular to the base AND splits the base in half

Base Angles: Have the same measure

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: Growth or rate of change.

y-intercept: Starting point on the y-axis. (0,b)

Slope y-intercept

Slope-Intercept Form

First plot the y-intercept on

the y-axis

Next, use rise over run to plot new points

Now connect the points with a line!

You can go backwards if necessary!

Parallel Lines (pg 47)

Parallel lines do not intersect.

Parallel lines have the same slope.For example:

y 52x 4

y 52x 1

Perpendicular Lines (pg 47)

Perpendicular lines intersect at a right angle.

Slopes of perpendicular lines are opposite reciprocals (opposite signs and flipped).

For example:

y x 2 13

Venn Diagram

#1: Has two or more siblings

#2: Speaks at least two languages

Venn Diagrams (pg 42)

Condition #1 Condition #2

Satisfies condition 1

Satisfies condition 2

Satisfies neither

conditionSatisfies both

conditions

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

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.

Example: What is the probability of selecting a heart from a deck of cards?

Number of Desired OutcomeseventTotal Possible Outcomes

Number of Hearts 13 1select 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 2-12Chapter 1 Individual Test Friday

m A m B m C

or m CAC 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 2-33Chapter 1 Individual Test – Is Thursday okay instead?

Notation for Angles

If there is only one angle at the vertex, you can also name the angle using the vertex:

Incorrect:

FEDDEF

Measure

Correct:

Incorrect:

45m DEF m A m B

45DEF A B

Angle Relationships (pg 76)Complementary Angles: Two

angles that have measures that add up to 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

60°x°

x° + y° = 90°

110° x° y°

x° + y° = 180°

x° y°

x° = y°

Marcos’ Tile Pattern

How can you create a tile pattern with a single parallelogram?

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.

b. What does this mean in terms of the angles in our pattern? Color all angles that must be equal the same color.

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.

Use the following diagram to help answer question 2-15.

Why Parallel Lines?

2-23 (a)

More Angles formed by Transversals

48°132°

132°132°

a. Alternate Interiorb. (1) Same Side Interior (2) (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 PropertyThe 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 )

( 3x – 2 )( 2x + 7)

= 6x2 + 17x – 14

+ 21x + -14 6x2

• Firsts• Outers• Inners • Lasts• Simplify

( x + 5 )( x + 3 )

+5x +15

x2 + 8x + 15

Box Method FOIL

Angles formed by Parallel Lines and a Transversal

Corresponding - Congruent

Alternate Interior - Congruent

Same-Side Interior - Supplementary

a a = b>

>100°

>ba a = b

>22°22°

>ba a + b = 180°

>60°120°

Triangle Angle Sum Theorem

The measures of the angles in a triangle add up to 180°.

Example:

mA mB mC 180

65°70°

57°57°123°

57°123°

123° 81°

81°99°

2-37: Challenge!fg

hkmpqrsuv

2-43 and 2-44

100°B

2-43 and 2-44

If Same-Side Interior angles are supplementary, then the lines must be parallel.

If Corresponding angles are congruent,

If Alternate Interior angles are congruent,

then the lines must be parallel.

80°100° 100°

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 2-65Optional EC: Problem 2-49 neatly done and

well- explained 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 2-85Check 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. b and d2. a and x3. d and w4. c and w

Possible Choices:5. x and y

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?

What about non-right triangles?10 cm

Where is the Height & BaseH

BaseBase

Obtuse Triangle

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.

Can We find the Area?

YES!YES!

Area of a Parallelogram

Rectangle!

Height

Area = b.h

The area of a parallelogram is the base times the height.

Area = b.hh

13 A = 20.5 = 100

Area of a Trapezoid

Height

Base Two

Base One

Parallelogram!

DuplicateReflectTranslateArea = (b1 + b2) h

Area of a Trapezoid

Area =

1 212b b h

The area of a trapezoid is half of the sum of the bases times the height.

Area of a Trapezoid

Area = h

4 5 A = ½ (9+15) 4 = ½ . 24 . 4 = 48

1 212b b h

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 2-104Optional 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

“Weight”

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 2-122Optional 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.

a – b < c < a + b

a – c < b < a + c

b – c < a < b + c

Longest Side: Slightly less than the sum of the two shorter sides

Shortest Side: Slightly more than the difference of the two shorter

Triangle Inequality

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 CL2-131Chapter 2 Individual Wednesday

The Pythagorean Theorem

a2 + b2 = c2

Pythagorean Theorem

a2 + b2 = c2a c

HypotenuseWhen to use it:• If you have a right triangle• You need to solve for a side length• If two sides lengths are known

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 3-21Chapter 2 Individual Wednesday

Dilation

A transformation that shrinks or stretches a

shape proportionally in all directions.

Enlarging

Similar Figures

Exactly same shape but not necessarily same size

• Angles are congruent• The ratios between corresponding sides

are equal

90°127°

53°90°

90°127°

Zoom FactorThe number each side is multiplied

by to enlarge or reduce the figure

Example:

Zoom Factor = 2

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 3-42Chapter 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:

7 ft 16.3 ft

Notation

ABC XY

m ABC XY

Angle ABC Line Segment 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

60 ft ? ft? ft? ft

720 in? in

? in? in

Writing a Similarity Statement

Δ Δ A ZZBC XYXY~

Example: ΔDEF~ΔRST The order of the letters determines which

sides and angles correspond.

Writing a Proportion

ABCD ~ WXYZ

=BCABAB

AB WXWX

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:

14 71 4x

Day 17: February 22nd

• 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:

Acceptable:

~AB CD

What Conjecture will we use:

SSS~ Facts

ConclusionΔCDF ~ ΔRTQ SSS~

Another Example

What Conjecture will we use:

m A m Z

AA~ Facts

m B m Y

ConclusionΔABC ~ ΔZYX AA~

60°100°

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 MondayChapter 3 Individual Test Wednesday

Conditions for Triangle SimilarityIf 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.SAS~

Two pairs of corresponding lengths have the same zoom factor and the angles between the sides have equal measure.

NO CONJECTURE FOR ASS~

55°40°

3070°

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 CL3-110Chapter 3 Individual Test Wednesday

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 4-10Chapter 3 Individual Test Tomorrow

Chapter 1-2 TopicsAngles:• Acute, Obtuse, Right, Straight, Circular – p. 24• Complementary, Supplementary, Congruent – p. 76• Vertical, Corresponding, Same-Side Interior, Alternate Interior

– Toolkit and p. 91Lines:• Slopes of parallel and perpendicular lines – p. 47Transformations:• Reflection, Rotation, Translation, and Prime Notation – p.81Shapes:• Name/Define shapes – ToolkitProbability:• Use proper notation…Ex: P(choosing a King) = 4/52 = 1/13

– Page 60

Chapter 1-2 TopicsTriangles:• Triangle Angle Sum Theorem – p.100• Area• Triangle Inequality TheoremArea:• Triangle, Parallelogram, Rectangle, Trapezoid, Square

– Page 112 and Learning Log/ToolkitPythagorean Theorem & Square Roots – p. 115 and 123

Chapter 3 TopicsDilations• Zoom Factor – p. 142Similarity• 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…

200 cmx cm

Eye Height Eye

Height

Lessons from Abroad

12 + 930 = 942

6 – 2 = 4

316 ft

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 4-47Chapter 4 Team Test Friday

Warm-Up! March 6th

10 in.

1. The area of the triangle below is 42 in2. Calculate DC.

2. Simplify: 68

Warm-Up! March 6th

Solve for x:

Trigonometry

Hypotenuse

(across from the 90° angle)

Adjacent

(forms the known angle)

Opposite

(across from the known angle)

Theta ( ) is always an acute angle

Trigonometry

Hypotenuse

(across from the 90° angle)

Adjacent

(forms the known angle)

Opposite

(across from the known angle)

Theta ( ) is always an acute angle

Trigonometry (LL) Theta ( ) is always an acute angle

Adjacent

Trigonometry (LL) Theta ( ) is always an acute angle

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 4-67Chapter 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

#41#28

ListenSTART

ReadWrite

Listen

ReadWrite

Listen

One Possibility:

Take Bus #41 and Listen to an MP3

player

ReadWrite

Listen

ReadWrite

Listen

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 4-86Chapter 4 Team Test TomorrowProblem 4-71 is optional extra credit (Get handout from Ms.

4-60: Tree Diagram

DoubleSTART $1500

Double

4-77: Area Diagram

Spinner #1

IT UT AT

IF UF AF

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 CL4-105Problem 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

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 5-20Bring circular food for tomorrow that you signed up forChapter 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

Trigonometry SohCahToa

sin( )

cos( )

tan( )

opposite ohypotenuse hadjacent ahypotenuse hopposite oadjacent 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

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.

You can use this

whenever a problem has an

equilateral triangle!

30° – 60° – 90°

Hypotenuse

Short Leg (SL)

30° – 60° – 90°Remember √3 because there are 3 different angles

You MUST know SL first!

SL Hyp÷√3

Isosceles Right Triangle 45° – 45° – 90°

Remember √2 because 2 angles are the same

Leg(s) Hypotenuse

÷√2

Isosceles Right Triangle 45° – 45° – 90°

A 45° – 45° – 90° triangle is half of a square.

45°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: Problems 5-67 to 5-72

Pythagorean TripleA 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

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 non-right 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 5-94Ch. 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 5-105Ch. 5 Team Test TomorrowMidterm (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 CL5-136Midterm (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: Problems 6-4 to 6-9 AND 6-13 to 6-18Midterm (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 SimilarityIf you are testing for similarity, you can use the

following conjectures:

SSS~All three corresponding side lengths have

the same zoom factorAA~

Two pairs of corresponding angles have equal measures.

SAS~Two pairs of corresponding lengths have

the same zoom factor and the angles between the sides have equal measure.

NO CONJECTURE FOR ASS~

55°40°

3070°

Conditions for Triangle Congruence

SSSAll three pairs of corresponding side

lengths have equal length.

ASATwo angles and the side between them

are congruent to the corresponding angles and side lengths.

SASTwo pairs of corresponding sides have

equal lengths and the angles between the sides have equal measure.

55°40°

If you are testing for congruence, you can use the following conjectures:

Conditions for Triangle Congruence

AASTwo pairs of corresponding angles and

one pair of corresponding sides that are not between them have equal measure.

HLThe 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

If you are testing for congruence, you can use the following conjectures:

42°51

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 6-40Chapter 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 6-12Complete 6-12 on page 295:

Use your triangle congruence conjectures to determine if the following pairs of triangles must be congruent.

SAS SSS

SAS ASSAASASA

Problem 6-12 ContinuedComplete 6-12 on page 295:

Use your triangle congruence conjectures to determine if the following pairs of triangles must be congruent.

AASSSS

AAAASS

Example 1

Determine if the triangles below are congruent. If the triangles are congruent, make a flowchart to justify your answer.

Example 2

Determine if the triangles below are congruent. If the triangles are congruent, make a flowchart to justify your answer.

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 6-48Midterm (Ch. 5 Individual Test) Tomorrow!

Day 43: March 30th

Objective: Assess Chapters 1-5 in an individual setting.

• 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 6-66Bring 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 7-Chapter 6 Individual Test Friday

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