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 LAI TUNG LEUNG SHING YIU MING SUM YEE FEI TSO KWOK LAI 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 ) Next page

Two triangles are similar if all their corresponding sides are proportional. XZ Y A B C (AB/XY) = (BC/YZ) = (CA/ZX)  ABC ~  XYZ (Abbreviation : 3 sides proportional) Next page

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.  ) Next page

I II non-similar The following are non-similar triangles Next page

III IV Next 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.A B.3 sides proportional C.2 sides proportional and included angle

3.Are the following triangles similar ? A L B C N M A. Yes B.No

3.Name the similar triangles and give reasons. 4 L N A B C M 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 M

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 M C.  ABC~  MNL (3 sides proportional) D.  ABC~  NLM (A.A.A)

5.Are the following triangles similar ? A. Yes B.No A B C 46º 8 7 P R Q 3.5 4

6.Name the triangles and give reasons. A.Yes B.No A 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 H B K C C.  AHK~  ACB(3 sides proportional) D.  AHK~  BAC(3 sides proportional)

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 A B C 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 Q R 3 xy

A B C P Q R10 6 c 5 4d 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 BC P Q R x y 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