Similarity
16
Similarity
description
Similarity. Triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. TESTS FOR SIMILARITY. Two triangles are similar if: All corresponding angles are equal All the corresponding sides have the same ratio (proportional). - PowerPoint PPT Presentation
Transcript of Similarity
SimilaritySimilarity
TESTS FOR SIMILARITY
Two triangles are similar if:
• All corresponding angles are equal• All the corresponding sides have the same ratio
(proportional)
Triangles are similar if their corresponding angles are equal and their corresponding sides
are proportional
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
Type 1: 3 angles of 1 triangle are the same as 3
angles of the other (AAA)
A
B C
D
E F
In triangle ABC, any 2 angles are equal to any 2 angles of triangle DEF, then they are similar.
g
h i
k
l
Angle g= angle k
Angle h= angle j
triangle ABC and DEF are similar
j
Angle i= angle l
Type 2: 3 pairs of corresponding sides are in
the same ratio
A
B C
z
h
i
D
EF
In triangle ABC and DEF, if
kz
kh
ki
triangle ABC and DEF are similar.
where k is a constant.
kAC
DF
BC
EF
AB
DE
Type 3: 2 pairs of corresponding sides are in the
same ratio and the included angle is equal (SAS) A
B
z
h
i
C
D
E
kz
kh
ki
F
triangle ABC and triangle DEF are similar.
g
h
In triangle ABC and DEF, if
kBC
EF
AB
DE
and angle g = angle h.
1. Are the following triangles similar? Not drawn to scale.
A
B
C
D
E
F
75
40
40
65
1. Are the following triangles similar? Not drawn to scale.
A
B
C
2
5
6
E
4
10
12
D
F
B
1
4
3.5
A
B
E
2
5
7.5
F
D
1. Are the following triangles similar? Not drawn to scale.
B
A
C
E
F
D
3.5
5
7
1055 55
1. Are the following triangles similar? Not drawn to scale.
Think!
1 Which of the following triangles are always similar?
a. right triangles
b. isosceles triangles
c. equilateral triangles
Similar triangles are exactly the same shape and size.
A) True
B) False
2.
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
3.
4. In the diagram, DE is parallel to AC. BD = 4, DA = 6 and EC = 8. Find BC to the nearest tenth.
A) 4.3
B) 5.3
C) 8.3
D) 13.3
5. Find BC.
A) 4
B) 4.5
C) 13.5
D) 17
6. 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?
A) 8.6
B) 16
C) 17.5
D) 20
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