Chinese University of Hong Kong

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Chinese University of Hong Kong

• Group Project Two

Communication and Technology
Dr. Fong Lok Lee
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Form One mathematics
Similar Triangle
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Target Audience Form one student(band three)
Type of software pre-lesson self learning
package
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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

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Cat mother, MiMi, lost her daughters, would you
please help her to find her daughters. Her
daughters have the similar footprint with their
mother.
MiMis footprint
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Contents
1. Introduction of Similar Figures
2. Introduction of Similar Triangles
3. Exercise of Similar Triangles
4. Summary of Similar Triangles
5. Member List
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Similar Figures

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

Similar figures
Non-similar figures
Continue
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The following are similar figures.
I
II
9
III
Back to Similar Figures
IV
V
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The following are non-similar figures.
I
II
11
III
Back to Similar Figures
IV
V
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Now can you find MiMis daughters?
MiMis footprint
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Similar Triangles

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

A
X
Next page
Z
Y
B
C
?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
A
C
Next page
Y
B
(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.

A
X
Next page
Y
Z
B
C
?A ?X, (AB/XY) (CA/ZX) ??ABC
?XYZ (Abbreviation ratio of 2 sides, inc. ?)
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The following are non-similar triangles
I
II
Next page
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III
Next page
IV
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1.
Which of the following is similar to the above
triangle?
B
A
C
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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
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3. Are the following triangles similar ?
L
A
A. Yes
B. No
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3. Name the similar triangles and give reasons.
L
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)
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4. Are the following triangles similar ?
A. Yes
B. No
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4. Name the similar triangles and give reasons.
A. ? ABC ? LMN (3 sides proportional)
B. ? ABC ? MNL (A.A.A)
C. ? ABC ? MNL (3 sides proportional)
D. ? ABC ? NLM (A.A.A)
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5. Are the following triangles similar ?
A. Yes
B. No
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6. Name the triangles and give reasons.
A
A. Yes
B. No
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6. Are the following triangles similar ? If
they are similar, name the triangles and give
reasons.
A
A. ? AHK ? ABC(A.A.A)
B. ? AHK ? ACB(A.A.A)
C. ? AHK ? ACB(3 sides proportional)
D. ? AHK ? BAC(3 sides proportional)
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7. Are the following triangles similar ?
A. yes
B. No
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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)
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8. In the figure, the two triangles are
similar. What are x and y ?
P
A. x 3.5 , y 4 B. x 3.5 , y 6 C. x 4 ,
y 3.5 D. x 4 , y 5
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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
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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
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SUMMARY
3 Conditions of Similar Triangles 1. 3 angles
equal 2. 3 sides proportional 3. 2 sides
proportional and included equal angles