Name ___________________________ Score ______ ______ ______

assignments notes spirit

Geometry – Unit 7 Similar Triangles January 2015

e = even problems only o = odd problems only 4 = every 4th problem (4, 8, 12, etc) Date Lesson Assignment Stamp At Home

Tues 1/06

Algebra Review

Worksheet View and fill in 8.7 notes

Wed 1/07 8.7 #1 Dilations worksheet

Complete Dilations

Assessment WS Thurs

1/08 8.7 #2 p. 509: 2, 3, 8 – 15, 20 – 23, 34 Constructing Dilations Worksheet (#1 & #2)

Fri 1/09 8.7/8.3 #3 Constructions worksheet View and fill in 8.3 notes

Mon 1/12 8.3 #4 p. 475: 1, 4 – 8, 11, 12, 16, 17,

19 – 23, 31, 35 – 40, 46, 47

Tues 1/13

Quiz 8.7 & 8.3 Cumulative Review

View and fill in 8.4/8.5a

notes Wed

1/14 8.4/8.5 #5

p. 483: 1, 3 – 5, 8, 10, 11, 18 – 26 (skip 20) p. 492: 1, 2, 3, 5, 8 – 12

View and fill in 8.4/8.5b notes

Thurs 1/15 8.4/8.5 #6 p. 483: 6, 7, 33 – 38, 39 – 47o

p. 493: 15 – 27 View and fill in 8.4/8.5c

notes Fri

1/16 8.4/8.5 #7 p. 484: 29, 30, 48, 50 – 53, 56, 58 – 60 p. 494: 29, 32 – 34

Mon 1/19

NO SCHOOL Martin Luther King Jr. Day

Tues 1/20 8.4/8.5 #8 Worksheet 8.4/8.5 Review WS

Wed 1/21

Quiz 8.4 & 8.5 Cumulative Review

Thurs 1/22 8.6 #9 Activity 8.6 View and fill in 8.6 notes

Fri 1/23 8.6 #10 p. 502: 1 – 10, 11 – 27o, 28, 34,

35 8.6 Review WS

Mon 1/26

Quiz on 8.6/Review Unit 7 Review WS

Tues 1/27 Review Unit 7 Review WS

Wed 1/28 Test

NOTE: If an assignment is not completed in class, it is your responsibility to complete the assignment for homework and have it checked the following day to receive full credit.

2

Assignment Format

3

Lesson 8.7: ________________________________________________________________________________ Goals: ____________________________________________________________________________________

Review →

Isometry: A _______________________ that preserves _________________. • Known as a “______________” transformation. • ________________, __________________ and ____________________.

Scale Factor: The ______________ of the ________________ of _________ corresponding _______________ for similar polygons.

• _______ is used to represent the scale factor. Dilation: A “__________________” transformation that maps a preimage onto an image that is _________________.

• Reduction – the ___________________________ comparing the __________ to the _____________ is between _____ and _____.

• Enlargement – the _________________________

comparing the _________ to the ______________ is greater than _____.

Ex: Determine whether the dilation from Figure A to Figure B is a reduction or an enlargement. Then find the values of the variables. Describing a Dilation: To describe a dilation state the following…

• ______________________ • _______________________________ – a ____________ point in the plane about

which all points are ___________________ or ____________________.

The ________________________ can be found by comparing corresponding ___________ lengths, or by comparing the _________________ from the _______________ to corresponding ______________. ______________ compare the ____________ to the ____________________.

4

Ex: Find the scale factor. Tell whether the dilation is a reduction or an enlargement.

Ex: Find the scale factor. Tell whether the dilation is a reduction or an enlargement. Then find the value of the variables.

Ex: Draw a dilation using the given center of dilation and scale factor. a. Center: 0,0( ) k = 5

3 b. Center: 0,0( ) k = 12

Summary What determines if a dilation is a reduction or an enlargement? …………………………………………………………………………………………………. …………………………………………………………………………………………………. How do you find the scale factor of a dilation? …………………………………………………………………………………………………. ………………………………………………………………………………………………….

Geometry 103Chapter 8 Resource Book

Copyright © McDougal Littell Inc. All rights reserved.

Practice CFor use with pages 506–513

8.7LESSON

NAME _________________________________________________________ DATE ___________

Lesson

8.7

Identify the dilation, and find its scale factor. Then, find the values ofthe variables.

1. 2.

3. 4.

Use the origin as the center of the dilation and the given scale factorto find the coordinates of the vertices of the image of the polygon.

5. 6.

7. You are making hand shadows on a wall using a flashlight. You hold yourhand 1 foot from the flashlight and 5 feet from the wall. Your hand is parallelto the wall. If the measure from your thumb to ring finger is 6 inches, whatwill be the distance between them in the shadow?

y

x1

1G

H

J

I

y

x1

1

M

N

L

k ! 52k ! 2

3

x

18.4

12.6

7.56P "

P

C

x

y

z

9 13.57

5

5

P "P

C

yx

9

43

6

P "

P

C

x

y

12.55

4

8

P "

P

C

5

Lesson 8.3: ________________________________________________________________________________ Goals: ____________________________________________________________________________________

Similar Polygons:

• Corresponding ______________ are ________________. • Corresponding ____________________ are _________________.

Ex: Are the figures similar? If so, write a statement of similarity.

Ex: Are the figures similar? If so, write a statement of similarity.

Ex: !ABCD ~!GBEF . Find y. Ex: The triangles are similar. Find x and y.

Perimeters of Similar Polygons: If two ________________ are ______________, then the _________ of their ________________ is __________ to the _______________________. Area of Similar Polygons: If two ________________ are ______________, then the _________ of their _____________ is the ______________ of the _______________________.

Statement of Proportionality

Statement of Similarity

A B

D C

E F

H G

6

Lesson 8.4/8.5a: ____________________________________________________________________________ Goals: ____________________________________________________________________________________

Angle-Angle Similarity Postulate ( _________ ): If two __________ of one triangle are

_____________ to two __________ of another triangle, then the triangles are ____________.

Side-Side-Side Similarity Theorem ( _________ ): If the _____________________ sides of ______ triangles are ____________________, then the triangles are ____________. Side-Angle-Side Similarity Theorem ( _________ ): If an __________ of one triangle is _____________ to an __________ of another triangle and the ____________ of the _______ that make these __________ are __________________, then the triangles are ____________. Ex: Determine whether the triangles can be proved similar. If they are similar, name the postulate or theorem that can be used to prove that the two triangles are similar. Then, write a similarity statement. If they are not similar, explain why. a. b.

c. d.

Geometry 71Chapter 8 Resource Book

Copyright © McDougal Littell Inc. All rights reserved.

Practice BFor use with pages 488–496

8.5LESSON

NAME _________________________________________________________ DATE ___________

Lesson

8.5Name a postulate or theorem that can be used to prove that the two

triangles are similar. Then, write a similarity statement.

1. 2. 3.

Are the triangles similar? If so, state the similarity and the postulateor theorem that justifies your answer.

4. 5.

Draw the given triangles roughly to scale. Then, name a postulate ortheorem that can be used to prove that the triangles are similar.

6. The side lengths of are 3, 4, and 6, and the side lengths of are6, 8, and 12.

7. In , In , and

8. In , In ,

Use the diagram shown to complete the statements.

9.

10.

11.

12.

13. perimeter perimeter

In Exercises 14 and 15, use the diagram at the right.

To determine the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the tree, as shown.

14. How tall is the tree?

15. Your little sister wants to see the top of the tree also. However, she is only 4 feet tall. Leaving the mirror 2 feet from her feet, how farfrom the base of the tree should the mirror be placed?

6 ft

2 ft 24 ft

!BEA ! ? !DEC:

EC ! ?

m"EBA ! ?

m"DEC ! ?

!AEB ~ ? A

D C

E

B

8

6

15

136"

60", XY ! 3, and YZ ! 6.m"Y !!XYZm"B ! 60", AB ! 6, and BC ! 12.!ABC

m"Z ! 85".m"Y ! 80"!XYZm"A ! 15" and m"B ! 80".!ABC

!XYZ!ABC

T S

D

R M X

20"

120"

120"

40"

A

F

D C

R

T

72"72" 10

15

914

H

F D

G

E

M N O

P

Q

B CX

Y ZA

6

6

4

9

70 GeometryChapter 8 Resource Book

Copyright © McDougal Littell Inc. All rights reserved.

Practice AFor use with pages 488–496

8.5LESSON

NAME _________________________________________________________ DATE ___________

Less

on

8.5

Name a postulate or theorem that can be used to prove that thetwo triangles are similar. Then, write a similarity statement.

1. 2. 3.

Determine which two of the three given triangles are similar. Findthe scale factor for the pair.

4.

5.

Are the triangles similar? If so, state the similarity and the postulateor theorem that justifies your answer.

6. 7.

Decide whether the statement is true or false. Explain your reasoning.

8. If an acute angle of a right triangle is congruent to an acute angle of anotherright triangle, then the triangles are similar.

9. All equilateral triangles are similar.

10. If two triangles are congruent, then they are similar.

11. If two triangles are similar, then they are congruent.

12. All isosceles triangles with a vertex angle are similar.40!

A R

SC M

TC

A

B

F E

D92!

57! 92!41!

QR

P

430!

M

O

N6

75!

J

L

K320!

G

HI

3.52

3

D

E

F

7

459!

6

A

B

C5

8

38!

7

M A

H U

T

CA B

E

D12

6

A V

Q

D

F

M

3

4

8

6

7

Lesson 8.4/8.5b: ____________________________________________________________________________ Goals: ____________________________________________________________________________________

Ex: △LMN ~△PQN . Write a statement of proportionality. Find m M∠ , m P∠ , and MN.

Ex: Explain why the triangles are similar. Then find EH.

Ex: Explain why the triangles are similar. Then find x.

Ex: The two triangles are similar. Find the value of x.

Ex: The two triangles are similar. Find the value of x.

Ex: Which two triangles are similar? Which postulate or theorem was used?

8

Lesson 8.4/8.5c: ____________________________________________________________________________ Goals: ____________________________________________________________________________________

Ex: Find the coordinates for point E so that ΔOBC ΔODE .

Given that 0 0,0( ), B 0,3( ), C 6,0( ), D 0,5( )

Given: DE ! AC Prove: △ABC ∼△DBE

Statement Reason

Given: AC = 6, CD = 4, BC = 9, CE = 6 Prove: △ABC ∼△DEC

Statement Reason

Ex: To measure the distance EF across the lake, a surveyor at S locates points E, F, G, and H as shown. What is EF? (write your answer in a complete sentence)

Copyright © by Holt, Rinehart and Winston. 25 Holt GeometryAll rights reserved.

Name Date Class

LESSON

7-3Problem SolvingTriangle Similarity: AA, SSS, and SAS

Use the diagram for Exercises 1 and 2.

In the diagram of the tandem bike, _

AE ! _

BD .

1. Explain why !CBD " !CAE.

2. Find CE to the nearest tenth.

3. Is !WXZ " !XYZ? Explain.

19.3

13.813

11

16.3

4. Find RQ. Explain how you found it.

24

44

40

25

27.5

Choose the best answer.

5. Find the value of x that makes !FGH " !JKL.

20

4

3.5

8

A 8 C 12B 9 D 16

6. Triangle STU has vertices at S(0, 0), T(2, 6), and U(8, 2). If !STU " !WXY and the coordinates of W are (0, 0), what are possible coordinates of X and Y?F X(1, 3) and Y(4, 1) G X(1, 3) and Y(2, 0)H X(3, 1) and Y(2, 4)J X(0, 3) and Y(4, 0)

7. To measure the distance EF across the lake, a surveyor at S locates points E, F, G, and H as shown. What is EF ?

A 25 m C 45 mB 36 m D 90 m

9

Lesson 4: _________________________________________________________________________________ Goals: ____________________________________________________________________________________

Triangle Proportionality Theorem: If a line _________________ two ____________ of a

triangle and is _______________ to the ___________ side, then the line ______________ the ________ sides ______________________. Triangle Proportionality Converse: If a line _________________ two ____________ of a triangle ______________________, then the line is _______________ to the ________ side.

Ex: UY !VX , UV = 3, UW = 18, and XW = 16. Label the figure with the given information then find YX. Ex: Determine whether the given information implies BC ! DE . Explain. a. b.

Parallel Lines and Proportional Transversal: If three ______________ lines ___________ two ________________, then the ________________are _______________ proportionally.

10

Ex: Use the figure to complete each proportion.

a. ABAF

= BC

b. ADBD

=CE

c. AG

= ABAF

d. AB = AC

EG

Ex: Find x.

Ex: Use the figure to determine if the statement is true or false. Explain.

a. ABBD

= ACCE

b. ECCA

= EDCB

c. ABAD

= ACAE

d. ABBD

= BCDE

Angle Bisector and Divided Sides: If a ray ______________ an ___________ of a triangle, then the _____________ of the ______________ of the ___________________ side are _____________________ with the _____________ of the other two ____________. Ex: ∠LKM ≅ ∠NKM . Find NM.

………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… …………………………………………………………………………………

………………………………………………………………………………… …………………………………………………………………………………

11