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Similar Figures in a Nutshell! (10 days)

To provide support for teachers who have concerns about being able tocomplete the Math 436 course objectives this year, a group of consultants hasprepared outlines which condense the work to be covered in three areas:statistics, similarity and trigonometry. These topics in a nutshell cover theessence of the objectives and provide the highlights needed by the students forMath 536. Please note that these are suggestions for the year only, and thatthis is less time than the MEQ curriculum allows for these topics.

Day

1

2

3

4

5

6

7

8 & 9

10

Topic

Dilatations (Similarity Transformations) and Composites

Properties of Similar Figures

Minimum Condition for Similar Triangles (SAS, SSS, AA)

Theorems dealing with Similarity (Principles from Appendixof MEQ Curriculum)

Perimeters and Areas of Similar Figures

Similar Solids

Surface Areas and Volumes of Similar Solids

Comprehensive Review

Test

__________A temporary solution for 1998-99 to cover the Math 436 course objectives.

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Similar Figures in a Nutshell (10 days)1998 - 1999

To help teachers cover all the objectives of the Math 436 course in 1998-99, itsfirst year of implementation, is the aim of the following breakdown. It is

suggested that the similarity part of Objective 2 To solve problems using theconcepts of isometry, equivalence and similarity. can be covered in 10 daysusing the outline below.

The content to be covered is summarized on page 412 of the textbook Mathematical Reflections 436 and on pages 28 - 29 of the MEQ curriculumdocument.

1. Dilatations (Similarity Transformations) and Composites (1 day)

Teaching Example: Spider Web and Beams activity p. 365

Exercises: p. 369 a (1 - 4), b, cp. 371 #1, 2p. 373 #1

Review Questions (MEQ June 436 Exam 1997) #8, 10

Comments: 1. Dilatation is a better term, rather than similaritytransformation. Dilatation is the term used for asimple enlargement or reduction.

2. A similarity transformation can be an isometry, adilatation or a composite of these transformations.

2. Properties of Similar Figures (1 day)

Teaching Example: p. 379 Activity 2 (and have the students recordthe 2 properties)

Comment: Corresponding sides (not lines) for property #2, p. 379.

Exercises: p. 382 #1, 2p. 385 #15 a, d, e; 16 a, b, d

3. Minimum Conditions for Similar Triangles (1 day)

Teaching Examples: Have the students record the statements ofTheorems 1, 2 and 3 on pages 393, 394 and 395respectively. The proofs could be a readingassignment.


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p. 401 #5 as a group activity to ensure studentsunderstand the cases for similar triangles.

Exercises: p. 401 #6p. 402 #8, 9

Review Questions (MEQ June 416 Exam 1998) #7

4. Theorems Dealing with Similarity (1 day)

Teaching Examples: Have the students record the statements ofTheorems 4, 5 and 6 on pages 396, 397 and 398respectively. The proofs could be a readingassignment.

Length of the blade, activity, part a, page 404

Exercises: p. 404 #1, 2p. 405 #3, 4p. 415 #14; 16 a, b

Comment: p. 415 #12 Determine the values of x and y (missing fromthe question).

5. Perimeters and Areas of Similar Figures (1 day)

Teaching Examples: p. 406 1 a #1, 2

Have the students record the statements of Theorems8 & 9 on pages 407 and 408. Proofs could be a readingassignment.

Exercises: p. 409 #1 a, cp. 410 #5, 6, 9, 10p. 411 #11

6. Similar Solids (1 day)

Teaching Examples: p. 388 a, b

Have the students record the definition of similarsolids at the bottom of page 388.

Comment: Corresponding elements (not lines) at bottom of page 388.


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Exercises: p. 390 #4p. 391 #5, 8, 10

7. Surface Areas & Volume of Similar Solids (1 day)

Teaching Examples: Review Statement of Theorem 9 on page 408.

p. 408 #1 a, b

Exercises: p. 410 #4 a p. 411 #13, 14

Review Questions (MEQ June 436 Exams 1997 & 1998)

1997: #11

1998: #10, 11

8. Comprehensive Review (2 days)

First Day: Assign and correct the following questions(group work and correction)

p. 416 #16 cp. 417 #21, 24

MEQ June 436 1997 Exam #23

MEQ June 436 1998 Exam #24

Second Day: Assign and correct the following questions(group work and correction)

p. 420 #1 a, b; 2 a, bp. 421 #5

MEQ June 416 Exam 1998 #6, 22

9. Test on Day 10


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MEQ June 436 1997 Exam 1


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Similar Figures in a Nutshell: Answer Key 1

1. Dilatations (Similarity Transformations) and Composites (1 day)

p. 369 a 1) h t 2) h r 3) h s 4) h grb The corresponding angles have the

same measure.c The measures of the corresponding

sides are proportional.p. 371 #1 r s

#2 h grp. 373 #1 a) T b) F c) T d) F

Review Questions (MEQ June Exam 1997) #8 D#10 B

2. Properties of Similar Figures (1 day)

Teaching Example: p. 379 #2 No, No and Yes in all 3 cases

Exercises: p. 382 #1 a) Yes b) No c) No d) No#2 a) T b) F c) T d) F

p. 385 #15 a) No d) Yes e) Yes

#16 a) m AD 1.4=

b) m AB 3.2 m E 10= =

d) m AD 7.86 mEF 8.4

3. Minimum Conditions for Similar Triangles (1 day)

Teaching Examples: p. 401 #5 a) SAS b) SSS c) AA d) AA

Exercises: p. 401 #6 a) SSS b) AA c) AA p. 402 #8 1 20

2 ACD (right ) &mBC

mCD

(corresponding sides)3 SAS

#9 SAS

Review Questions (MEQ June 416 Exam 1998) #7 D


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4. Theorems Dealing with Similarity (1 day)

Teaching Examples: Length of the blade, part a mDF 31.25= cm

Exercises: p. 404 #1 mEB 5.3

#2 mDE 11.2=

p. 405 #3 mDE 3.75=

#4 a) mEF 3.3 b) mGH 6.6p. 415 #14 31.52

#16 a) 112.5 m b) 33.6 m

5. Perimeters and Areas of Similar Figures (1 day)

Teaching Examples: p. 406 1 a) #11

2,

1

2,

1

4

#2

1

3,

1

3,

1

9

Exercises: p. 409 #1 a)4

3,

4

3,16

9c)

5

4,

5

4,

25

16p. 410 #5 a) 17.44 c) 7.2 and 10.08

#6 62.5 cm#9 $347.22

#10 6.6 mp. 411 #11 18 m2

6. Similar Solids (1 day)

Teaching Examples: p. 388 a) No b) They are similar - the measuresof their corresponding elements are proportional.


2or

2

1b)

3

5or

5

3p. 390 #5 No (measures of corresponding

elements are not proportional)#8 Yes#10 No (measures of corresponding

elements are not proportional)


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7. Surface Areas & Volume of Similar Solids (1 day)

Teaching Examples: p. 408 #1 a) 1; 8; 64 b)1

8;

1

8


5,

4

5,

16

25and

64

125p. 411 #13 82.944 cm3

#14 r = 4.8 cm T.A. 337.784 cm2

Review Questions (MEQ June 436 Exams 1997 & 1998)

1997: #11 D

1998: #10 C#11 B

8. Comprehensive Review (2 days)

First Day: p. 416 #16 c) 200 m

p. 417 #21 m AB 100 m= ;m BC 125 m= ;

mCD 175 m=

#24 a) similar b) equivalent c)16

25

d)4

5

MEQ June 436 1997 Exam #23 43 cmMEQ June 436 1998 Exam #24 48 cm

Second Day: p. 420 #1 a) h r b) h s

#2 a) SAS; mFK 9.3 b) AA; mAB 10.5=

p. 421 #5 a) 9 cm b) 203.58 cm2 c)125

27

MEQ June 416 Exam 1998 #6 A

#2234


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