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Unit Vocabulary List (Highlight the words as they appear in the Unit)

Math 2 2017 Have a Good Day! Ms. J. Blackwell, nbct 1

Math 2Ms. J. Blackwell, nbct

https://sites.google.com/site/blackwellsbutterflyworld/homeUnit 1 – Geometric Transformations and Similarity

Day Date Topic Homework1 1/25Wed Translations & Reflections

Jan 24th – National Compliment Day

HW 1

2 1/26 Thurs RotationsNational Peanut Brittle Day

HW 2

3 1/27 Fri Combinations of MotionNational Chocolate Cake Day

HW 3

4 1/30 Mon Similarity HW 45 1/31Tues Dilations

(January is National Hot Tea & Soup Month)

HW 5

6 2/1 Wed Quiz Project7 2/2 Thurs Super Hero Project Plan Day

Ground Hog Day Review Evens

8 2/3 Fri Super Hero ProjectNational Wear Red & Carrot Cake Day

Review Odd

9 2/6 Mon Review & Project Plan DayNational Frozen Yogurt Day

Study & Triangle Vocab Pages 1 & 2 due Thurs

10 2/7 Tues Project Presentation Day & Review

Study

11 2/8 Wed Unit Test 1Say Something Nice to 3

People!

https://sites.google.com/site/blackwellsbutterflyworld/home

Translations Transformation Reflection RotationDilation Similarity Isometry Image

Pre - Image Composition Function Ratio

Unit 1 – Geometric Transformations & SimilarityMs. June L. Blackwell, nbct Keep track of your progress on each concept by checking the appropriate box as we go through the unit.

Concept List Know a little Need Practice I Got it!

1 Describe & Graph Translations

2 Describe & Graph Reflections

3 Describe & Graph Rotations

4 Calculate Similarity Ratios

5 Know The Difference Between Translations & Transformations

6

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Sta

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G-CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as

outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

G-CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describes the rotations and reflections that carry it onto itself.

G-CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

G-CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of

transformations that will carry a given figure onto another.G-MG.3 Apply geometric methods to solve design problems.

G-SRT.T Verify experimentally the properties of dilations given by a center and a scale factor.

Unit Reflection: (Specific items to review)

Transformation Graphic Organizer – Watch Video Clip and take notes


Definition Real – Life Examples

Picture Additional Information




Reflection

Rotation



Reflect, Translate & Rotate your initials below:

Class Notes

3 Types of Transformations


Translation

___________________ ___________________ _______________________

a. Guess the type of Transformations for the following problems.b. List the Pre – image and Image co –ordinates.c. Describe the pattern from pre – image to image.d. State the Algebraic Rule for the transformation.

1. 2.a. a.

b.Pre – image Image

X X’

Y Y’

Z Z’


J J’

K K’

L L’

c. c.

d. (x, y) ( , )

d. (x, y) ( , )


3.4.

a. a.


A A’

B B’

C C’


E E’

F F’

G G’

c. c.

d.

(x, y) ( , )

d.

(x, y) ( , )

Your Turn!


5.

6. Create a 5 letter label

a. a.

b.

Pre – image ImageP P’

Q Q’

R R’


c. c.

d.(x, y) ( , )

d.(x, y) ( , )


7. 8. Create a 3 letter label

a. a.

b.

Pre – image ImageP P’

Q Q’

R R’

S S’

b.

Pre – image Image

c. c.

d.(x, y) ( , )

d.(x, y) ( , )

HW 1 – Translations and ReflectionsThe point A (3, -6) is translated left 4 units and up 6 units

1. What are the coordinates of A’? __________


2. Write a rule for the translation ____________________

The point B (-5, 4) is translated down 5 units and right 2 units.

3. What are the coordinates of B’? __________

4. Write a rule for the translation ___________________

_

5. The point C’ ( 0, 7) is the result of translating a point up five units and left 2 units. What were the coordinates of

the original point? __________

6. The point D (11, 3) is translated to become the point D’ (6, 9). What is the rule for the translation between these

two points? ____________________

For each of the following problems reflect the point E (3, -7) over the given line. Then, a) find the coordinates for the image and b) write a rule for the transformation

7. Reflect over x – axis

a.

b. __________ c. __________8. Reflect over the line y = -x

a. __________ b. __________

9. Reflect over the line x = -2

a. __________ b. __________

For each of the following problems reflect the point F (-5, -2) over the given line. Then, a) find the coordinates for the image and b) write a rule for the transformation

10. Reflect over y – axis

a. __________ b. __________11. Reflect over the line y = x

a. __________ b. __________

12. Reflect over the line y = 3

a. __________ b. __________


Class work – Math is fun website

90 Degree Counter – clockwise 180 Degree Counter - clockwiseb.

Pre – image Imageb.

Pre – image Image

c. (x, y) ( , )

c. (x, y) ( , )


270 Degree Counter – clockwise Your Choice - ______ Degree Counter - clockwise



c. (x, y) ( , )

c. (If Possible)

(x, y) ( , )

Desmos Rotation Chart:


HW 2 – Rotations - # 1 - 12 Graph the preimage and image. List the coordinates of the image. Give the algebraic rule.1) ΔRST: R(2, -1), S(4, 0), and T(1, 3) 2) ΔFUN: F(-4, -1), U(-1, 3), and N(-1, 1)90° counter clockwise about the origin. 180° clockwise about the origin.

R’ (___,___)S’(___,___) T’(___,___)

F’ (___,___) U’(___,___) N’(___,___)

Rule : (x,y)→____________________ Rule : (x,y)→____________________

3) ΔTRL: T(2, -1), R(4, 0), and L(1, 3) 4) ΔCDY: C(-4,2), D(-1, 2), and Y(-1, -1)90° clockwise about the origin. 180° counter clockwise about the origin.

T’ (___,___) R’(___,___) L’(___,___)

C’ (___,___) D’(___,___) Y’(___,___)

Rule : (x,y)→____________________ Rule : (x,y)→____________________

5) ΔSCR: S(-3,1), C(-1,3), and R(-1,-1) 6) ΔSCR: S(-3,1), C(-1,3), and R(-1,-1) 270° clockwise about the origin 270° counter clockwise about the origin

S’ (___,___) C’(___,___) R’(___,___)

S’ (___,___) C’(___,___) R’(___,___)

Rule : (x,y)→____________________ Rule : (x,y)→____________________


7. Write a rule for a transformation that moves a point down six units and right 4 units.

____________________8. What are the six different lines (or types of lines) that you need to be able to reflect

across

__________________________________________________

9. Solve for y

3 x+5 y=86 x=36 __________

10.Give two differences between a clockwise and a counter clockwise rotation

________________________________________________________________

_______________________________________________________________

11.Reflect the point (3,6) over the line y=x

________

12.Solve for y

4 x+5 y=7−4 x+9=17 __________

13

Class work

1) Translate QRS if Q(4,1), R(1,-2), S(2,3) 2)Reflect Q’R’S’ if Q’(1,-3), R’(-2,-6), by the rule (x , y) (x – 3, y – 4). and S’(-1,-1) over the x-axis.

3) Rotate CAR if C(-1,-4), A(2,6), R(-4,-2) 4) Dilate C’A’R’ if C’(1,4), A’(-2,-3),

around the origin. and R’(3,2) over the line y = x.

5) What did you notice in problems 1&2 and problems 3&4? How were the shapes related? Explain how you could transform QRS by translating it left 3 and down 4 and then reflecting the image over the x-axis. Where does the final image end up?

6) How would you rotate CAR about the origin and then reflect it over the line y = x?

14

Combinations of Motion – Part 1

15

Combinations of Motions – Part 2

For # 1, 2, 5, & 6, there is a composition of motions given. Using the rules transformations, find the image of the point A (-1, 3) and come up with a new rule after both transformations have taken place.

1) Translate point A 4 units right and 2 units up, and then reflect that point over the line y = x.

A’ ______________ A ‘’ _________________Rule (x,y) →_____________________________

2) Rotate point A 90 degrees counter clockwise, and then translate the point right 5 and up 2.

A’ ______________ A ‘’ _________________Rule (x,y) →_____________________________

Now you are going to try some multiple transformations:

3) Translate ALT if A(-5,-1), L(-3,-2), T(-3,2) 4)Reflect TAB if T(2,3), A(1,1), by moving it right 6 and down 3, then reflect the and B(4,-3) over the x-axis, then reflectimage over the y-axis. the image over the y-axis.

5) Translate point A 4 units left and 2 units down, and then reflect that point over the y-axis.

A’ ______________ A ‘’ _________________Rule (x,y) →_____________________________

6) Rotate point A 90 degrees clockwise, and then reflect over the line y = -x.

A’ ______________ A ‘’ _________________Rule (x,y) →_____________________________

16

HW 31) Rotate ALT if A(-5,-1), L(-3,-2), T(-3,2) 2)Reflect TAB if T(2,3), A(1,1),

clockwise around the origin, then reflect the and B(4,-3) over the y-axis, then translateimage over the x-axis. the image by moving it right 2 and down 1.

3 Rotate ALT if A(-5,-1), L(-3,-2), T(-3,2) 4)Reflect TAB if T(2,3), A(1,1), clockwise around the origin, then reflect and B(4,-3) over the x-axis, then

translatethe image over the y-axis. the image by moving it left 5 and down 4.

5) Translate point A 4 units right and 2 units down, and then reflect that point over the x-axis.

A’ ______________ A ‘’ _________________Rule (x,y) →_____________________________

6) Rotate point A 180 degrees counter clockwise, and then reflect over the x-axis.

A’ ______________ A ‘’ _________________Rule (x,y) →_____________________________

7) Translate point A 4 units left and 2 units up, and then reflect that point over the line y = x.

17

A’ ______________ A ‘’ _________________Rule (x,y) →_____________________________

8) Rotate point A 180 degrees clockwise, and then translate down 6 units and right 4 units.

A’ ______________ A ‘’ _________________Rule (x,y) →_____________________________

Class work – Similarity

Similar Figures: Notated: ______ Similar figures are 2 figures that have the _______________________, but a ____________________________.

Their ______________________ angles are ____________________.

Their ______________________ sides are __________________________.

Example #1.Given: ABCD ~ EFGHThen:1) m∠E=¿¿ because ___________________________________________________________

2) ABEF

= AD?

Example #2.Determine if the triangles are similar.

Example # 3 Are the triangles similar?

Example # 4 Are the figures similar?

18

Big Sides:_________________

Medium Sides:_________________

Small Sides:__________________

#1 Given LMNO ~ QRST, find the value of x.

#2 Given the following similar triangles, find x and y.

#3 Given the following similar figures, find x and y.

#4 Given the following similar figures, solve for x.

# 5 Given the following similar figures, solve for x.

To find the Scale Factor: pick a pair of corresponding sides and calculate ________________________.

Math 2 2016 Smile & Have a Good Day! Ms. J. Blackwell, nbct 20

#6 Find the scale factor.




HW 4 # 1 - 11

Write a proportion to find each missing measure. Then, solve the proportion and find x.


9.The following diagram shows two similar rectangles:

(a) What is the scale factor from rectangle EFGH to rectangle ABCD? __________

(b) What is the length of side CD? __________

10. The following diagram shows two similar triangles:

(a) What is the scale factor from triangle ABC to triangle DEF? __________

(b) What is the length of side EF? __________

(c) What is the perimeter ratio from triangle ABC to triangle DEF? __________

11. The following diagram shows two similar triangles:

(a) What is the length of side GE? __________

(b) What is the scale factor from triangle EFG to triangle ABD? __________


Dilations - HW 5 = Part 1 & Part 2State whether a dilation using the scale factor, k, results in a reduction or an enlargement of the original figure.

1. k = 32. k = 1/33. k = 0.93 4. k = 5/4


Part 2

Determine if the following scale factor would create an enlargement, reduction, or isometric figure.

11. 3.5 12. 2/5 13. 0.6 14. 1 15. 4/3 16. 5/8

Given the point and its image, determine the scale factor.

17. A(3,6) A’(4.5, 9) 18. G’(3,6) G(1.5,3) 19. B(2,5) B’(1,2.5)

20. The sides of one right triangle are 6, 8, and 10. The sides of another right triangle are 10, 24, and 26. Determine if the triangles are similar. If so, what is the ratio of corresponding sides?

Class workUsing Reflections in Miniature Golf

Use reflections to draw the path of the ball from the tee (T) to the hole (H) for each golf hole below.

1. 2.


9 10

H

HT

T

T

H

3. 4.

5. 6.

7. 8.

Unit 1 – Math 2 Test Review – # 1 - 36

For each transformation, state the coordinates of the image of the point (1 , 4) and the general rule for the image of the point (x , y ).


HH

H

H

HT

T

T

T

T

A

C

B

D

A

C

B

D

A

C

B

D

For each of the following, graph and label the image for each transformation described.

10. Reflect over the y-axis 11. Rotate 180° about the origin 12. Translate right 4 units & down 3 units

Perform each of the transformations using ∆ABC below for #13 – 16.

A (7, –4), B (0, 6), C (–2, 3)

13. Reflect over the x-axis

15. Reflect over the line y = x

14. Rotate 90◦ counter-clockwise about the origin

16. Dilate about the origin by a magnitude of ½


A’__________B’__________C’__________

A’__________B’__________C’__________

A’__________B’__________C’__________

A’__________B’__________C’__________

Image of (1 , 4) Image of (x , y )

1. Reflect over y-axis

2. Reflect over x-axis

3. Reflect over y=x

4. Reflect over y=−x5. Reflect over y=26. Reflect over x=−27. Rotate 90 ° clockwise about the origin8. Rotate 90 ° counter-clockwise about the origin9. Rotate 180 ° about the origin

D'

C'

A'

B'

OA

D

C

B

State whether the specified pentagon is mapped to the other pentagon by a reflection, translation, or rotation

17. Pentagon 1 to Pentagon 3_______________________





Answer each of the following. 22. If translation T : (5 ,−3 ) → (−4 ,0 ), then T : (8 ,2 ) → (¿¿ )

23. T : ( x , y )→ ( x−5 , y+2 ), if F’ (7 ,−6) , find F. ________________

24. M is reflected over the y-axis. If M’ is (6 ,−1) , find M. ________________

25. C is rotated about the origin 90°. If C’ is (−9 , 5), find C. ________________

26. Y is rotated about the origin 180°. If the image of Y is (0, -3) find Y. ________________

27. A figure is reflected over the line y=−x. If the preimage is (2, 7), find the image. ____________

28. ∆ ABChas vertices A (5 ,−2 ) , B (−4 , 0 ) , C(7 ,1). Find the coordinates of the image of the triangle if it is dilated about the origin by a magnitude of 3.

A’( _____, _____ ), B’( _____, _____ ), C’( _____, _____ )

29. ABCD is dilated about point O by a magnitude of 2 to produce A’B’C’D’. The lengths of the segments of the preimage are as follows:

AB = 6, BC = 5, CD = 3, AD = 4

a. What is the length of B’ C ’?

b. What is the length of A ’ B ’?

30. For each problem, there is a composition of motions. Using your algebraic rules, come up with a new rule after both transformations have taken place.

a. Translate a triangle 5 units left and 3 units up, and then reflect the triangle over the x-axis.

29

1

65

43

2

9

1521

28

C

A

B

E

D

15

618

y

x

25

40

b. Rotate a triangle 90 degrees counter clockwise, and then reflect in the line y = x.

c. Reflect in the y-axis, and then translate right 4 units and down 2 units.

34. Quad. I Quad. II. Complete each part using the similar quadrilaterals.

a. The scale factor of Quad. I to Quad. II is ________.

b. Quad. STAR Quad. ________.

c. x = ________

d. y = ________

35. Δ BAC Δ DEC

a. What is the scale factor of Δ BAC to Δ DEC? _________

b. Find AC. _________

c. Find DE. _________

Find the value of x.36. x = _________ 37. x = _________

30

Quad. IIQuad. I

A

R

T

S F M

L

I

x

1612

14

20

x

30

30

12

1220

HW 1 – pages 30 - 32 Math 2 – Unit 2: Triangles – Triangle SumsParts of a Triangle:

Triangle – _______________________________

Name – _______________

Sides – _______________

Vertices – _______________

Angles – _______________

Classifying Triangles by Angles:

Acute ∆ Obtuse ∆ Right ∆ Equiangular ∆

Classifying Triangles by Sides:

Scalene ∆ Isosceles ∆ Equilateral ∆

Example #1: Identify the indicated type of triangle in the figure.

a.) two different isosceles triangles

b.) at least one scalene triangle

31

56

20

D

B

A C

Angle Sum Theorem:

The sum of the measures of the interior angles of a ___________________ is __________.

Vertical Angles Linear Pairs

Definition

Picture

Rule

Example #1: Find the missing angle measures. #2: Find the missing angle measures.

#3

32

A

C

B55 27

DFind m∠ A = Find

m∠DCB =

Math 2 – Spring 2016 Have a Good Day! Ms. J. Blackwell, nbct 33

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