1. Similarity

2. TESTS FOR SIMILARITY Two triangles are similar if:
All corresponding angles are equal
All the corresponding sides are proportional
Triangles are similar if their corresponding angles are equal and their corresponding sides are proportional

3. How To Identify？ Two triangles are similar if:
3 angles of 1 triangle are the same as 3 angles of the other
3 pairs of corresponding sides are in the same ratio
2 pairs of corresponding sides are in the same ratio and the included angle is equal

4. Tests for similarity of 2 triangles
Type 1: 3 angles of 1 triangle are the same as 3
angles of the other (AAA) D A
In triangle ABC, any 2 angle is equal to any 2 angles of triangle DEF, then they are similar. k g l j i h F C E B
Angle g= angle k
Angle h= angle j
Angle i= angle l
 triangle ABC and DEF are similar

5. Test for similarity between 2 triangles
Type 2: 3 pairs of corresponding sides are in
the same ratio D A
In triangle ABC and DEF, if z i kz ki
where k is a constant. B C h F E kh
 triangle ABC and DEF are similar.

6. Tests for similarity between two triangles
Type 3: 2 pairs of corresponding sides are in the
same ratio and the included angle is equal (SAS) D A
In triangle ABC and DEF, if kz z i ki g
and angle g = angle h. C h B h F E kh
 triangle ABC and triangle DEF are similar.

7. Question Are the following triangles similar? Not drawn to scale. A D40 40 75 E 65 B F C
Ans: yes

8. Question Are the following triangles similar? Not drawn to scale. D A12 6 4 2 F C B E 10 5
Ans: yes

9. Question Are the following triangles similar? Not drawn to scale. A D
7.5
3.5 2 1 B F B 4 E 5
Ans: no

10. Question Are the following triangles similar? Not drawn to scale. D A
3.5 10 55 55 F C B 5 E 7
Ans: yes

11. Think! 1 Which of the following triangles are always similar?
a.  right triangles
b.  isosceles triangles
c.  equilateral triangles
Ans:C

12. 2. Similar triangles are exactly the same shape and size. A) True
B) False
Ans:B

13. 3.
The sides of a triangle are 5, 6 and 10.  Find the length of the longest side of a similar triangle whose shortest side is 15.
A)10
B)15
C)18
D)30
Ans:D

14. In the diagram, DE is parallel to AC. BD = 4, DA = 6 and EC = 8. 4.
In the diagram, DE is parallel to AC.   BD = 4, DA = 6 and EC = 8. 
Find BC to the nearest tenth.
4.3
5.3
8.3
13.3
Ans: D

15. Find BC. 5. 4
4.5
13.5 17
Ans:C

16. At a certain time of the day, the shadow of a 5' boy is 8' long
At a certain time of the day, the shadow of a 5' boy is 8' long.  The shadow of a tree at this same time is 28' long.  How tall is the tree? 6.
8.6 16
17.5 20
Ans:C