# G17Edd5161R

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```					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       Non-similar       Continue
figures         figures
The following are similar figures.

I

II
III

Back to
Similar Figures

IV

V
The following are non-similar figures.

I

II
III

Back to
Similar Figures
IV

V
Now can you find MiMi’s daughters?

MiMi’s
footprint
Similar Triangles
• Two triangles are similar if all their
corresponding angles are equal.

X                           A

Next page
Y       Z
B             C
A= X, B= Y, A= Z ABC ~ XYZ
(Abbreviation : equiangular s )
• Two triangles are similar if all their
corresponding sides are proportional.

X          Z          A                 C

Next page
Y

B
(AB/XY) = (BC/YZ) = (CA/ZX) ABC ~ XYZ
(Abbreviation : 3 sides proportional)
• Two triangles are similar if two pairs of
their sides are proportional and their
included angles are equal.

A
X

Next page

Y          Z
B            C

A= X, (AB/XY) = (CA/ZX)           ABC ~ XYZ
(Abbreviation : ratio of 2 sides, inc. )
The following are non-similar triangles

I

II

Next page
III

Next page
IV
1.

Which of the following is similar to the
above triangle?
A               B                C
2. Give the reason for why the following triangles are similar?

A.     A.A.A
B.     3 sides proportional
C.     2 sides proportional and included angle
3.   Are the following triangles similar ?

L
B
8
3           3.5
7                  C
6
A                       M           4         N
A.      Yes
B.     No
3.   Name the similar triangles and give reasons.

L
B
8
3             3.5
7                   C
6
A                        M        4              N
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 ?

L
A

C
47º
47º
B                        M
N
A.         Yes
B.         No
4.   Name the similar triangles and give reasons.

L
A

C
47º
47º
B                         M
N
A.          ABC~  LMN (3 sides proportional)
B.          ABC~  MNL (A.A.A)
C.          ABC~  MNL (3 sides proportional)
D.          ABC~  NLM (A.A.A)
5.   Are the following triangles similar ?

P

A                       46º

46º                4
8                                  R
C
7                      3.5
B
Q

A.       Yes
B.       No
6.   Name the triangles and give reasons.

A

H       51º   K

C

51º
B
A.    Yes
B.    No
6.   Are the following triangles similar ?
If they are similar, name the triangles and give reasons.
A

H       51º     K

C

51º
B
A.      AHK~  ABC(A.A.A)
B.      AHK~  ACB(A.A.A)
C.      AHK~  ACB(3 sides proportional)
D.      AHK~  BAC(3 sides proportional)
7.   Are the following triangles similar ?

35º                          35º

A.      yes

B.      No
7.            Name the similar triangles and give reason.
A

C
B                                   D
35º                         35º

E

A.         ABC ~ CDE (AAA)
B.         ABC ~ EDC (AAA)
C.         ABC ~ CDE (3 sides proportional)
D.         ABC ~ EDC (3 sides proportional)
8.       In the figure, the two triangles are similar.
What are x and y ?
P
A
7
y       x
6
C           Q       3    R
B              8

A.        x = 3.5 , y = 4
B.        x = 3.5 , y = 6
C.        x = 4 , y = 3.5
D.        x=4,y=5
9.       In the figure, the two triangles are similar.
What are c and d ?
A
5
10                         P                      R
c                    4            d
B
Q
6
C

A.           c = 8.5 , d = 3
B.           c = 8.5 , d = 6
C.           c=8,d=6
D.           c=8,d=3
10.   In the figure, the two triangles are similar.
What are x , y and z ?
P
A

z                             x             8
y

B       3    C                              R
Q        6

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

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