Chinese University of Hong Kong

Group Project Two

Communication and Technology

Dr. Fong Lok Lee

Form One mathematics

Similar Triangle

Target Audience:Form one student(band three)

Type of software:pre-lesson self learning package

Name List of Group 17

98035520 LAI TUNG LEUNG

98036360 SHING YIU MING 98115710 SUM YEE FEI

98036440 TSO KWOK LAI

98041540 YEUNG PUI SHAN RITA

Cat mother, MiMi, lost her daughters, would you please help her to find her daughters. Her daughters have the similar footprint with their mother.

MiMi’s footprint

Contents

1. Introduction of Similar Figures

2. Introduction of Similar Triangles

3. Exercise of Similar Triangles

4. Summary of Similar Triangles

5. Member List

Similar Figures

Two figures are similar if they have the same shape but not necessary the

same size.

Similar figures

Non-similar figures

Continue

The following are similar figures.

I

II

III

IV

V

Back to

Similar Figures

The following are non-similar figures.

I

II

III

IV

V

Back to

Similar Figures

Now can you find MiMi’s daughters?

MiMi’s footprint

Similar Triangles

• Two triangles are similar if all their corresponding angles are equal.

A

B C

X

Y Z

A= X, B= Y, A= Z ABC ~ XYZ

(Abbreviation : equiangular s )

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• Two triangles are similar if all their corresponding sides are proportional.

X Z

Y

A

B

C

(AB/XY) = (BC/YZ) = (CA/ZX) ABC ~ XYZ

(Abbreviation : 3 sides proportional)

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• Two triangles are similar if two pairs of their sides are proportional and their included angles are equal.

Y

X

Z

A

B C

A= X, (AB/XY) = (CA/ZX) ABC ~ XYZ

(Abbreviation : ratio of 2 sides, inc. )

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I

II

The following are non-similarnon-similar triangles

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III

IVNext page

A B C

1.

Which of the following is similar to the above triangle?

2. Give the reason for why the following triangles are similar?

A. A.A.AB. 3 sides proportionalC. 2 sides proportional and included angle

3. Are the following triangles similar ?

A

LB

C7

6

8

4 NM

3.53

A. Yes

B. No

3. Name the similar triangles and give reasons.

4

L

NA

B

C7

6

8

M

3.53

A. ABC ~ LNM (3 sides proportional)

B. ABC ~ MLN (3 sides proportional)C. ABC ~ LNM (A.A.A)D. ABC ~ MLN (A.A.A)

4. Are the following triangles similar ?

A. Yes

B. No

A

B

C

47º

L

N

M47º

4. Name the similar triangles and give reasons.

A. ABC~ LMN (3 sides proportional)

B. ABC~ MNL (A.A.A)

A

B

C

47º

L

N

M47º

C. ABC~ MNL (3 sides proportional)

D. ABC~ NLM (A.A.A)

5. Are the following triangles similar ?

A. Yes

B. No

A

B

C46º

8

7

P

R

Q

46º

3.5

4

6. Name the triangles and give reasons.

A. Yes

B. No

A

51º

51º

H

B

K

C

6. Are the following triangles similar ?If they are similar, name the triangles and give reasons.

A. AHK~ ABC(A.A.A)

B. AHK~ ACB(A.A.A)

A

51º

51º

H

B

K

C

C. AHK~ ACB(3 sides proportional)

D. AHK~ BAC(3 sides proportional)

35º 35º

7. Are the following triangles similar ?

A. yes

B. No

7. Name the similar triangles and give reason.

A. ABC ~ CDE (AAA)

B. ABC ~ EDC (AAA)

C. ABC ~ CDE (3 sides proportional)

D. ABC ~ EDC (3 sides proportional)

35º 35º

A

BC

D

E

P

8. In the figure, the two triangles are similar.

What are x and y ?

A. x = 3.5 , y = 4

B. x = 3.5 , y = 6

C. x = 4 , y = 3.5

D. x = 4 , y = 5

B

A

C

6

7

8Q R3

xy

A

B

C

P

Q

R10

6

c

5

4 d

9. In the figure, the two triangles are similar.

What are c and d ?

A. c = 8.5 , d = 3

B. c = 8.5 , d = 6

C. c = 8 , d = 6

D. c = 8 , d = 3

A

B C

P

Q R6

8

3

xy

z

10. In the figure, the two triangles are similar.

What are x , y and z ?

A. x = 10 , y = 4 , z = 5

B. x = 10 , y = 4 , z = 20

C. x = 10 , y = 16 , z = 5

D. x = 10 , y = 16 , z = 20

SUMMARY

3 Conditions of Similar Triangles :

1. 3 angles equal

2. 3 sides proportional

3. 2 sides proportional and included equal angles