Download (D2) SN Similar Polygons

Similarity 2
Pre-AP Geometry Notes:
Focus: Similar Polygons
Name ____________________
Period _______ Date ________
Yesterday – You discovered the following. Fill in the blanks.
Two polygons are similar if their corresponding angles are ______________ and the lengths
of corresponding sides are _____________________.
Symbol for similarity: _____________________________
Example 1: Are these triangles similar?
B
X
110o
3 30o
2
7.5
5
4
A
40o
30o
Z
C
Y
10
___: are all 3 pairs of corresponding angles congruent?
___: are all 3 sides proportional?

ABC ~
XYZ
The common ratio between all three sides is called the ______________.
Example 2: The scale factor in example 1 is _______
Similarity Statements:
A
A) If polygon ABCDE ~ polygon FGHIJ, then
A  ___, B  ____, C  ___, D  ___, and
AB BC CD DE AE




E  ____. Also,
.
FG
B)
AB
 ________
FG
6
B
G
E
12
D
C
4
F
8
J
H
I
BC
 ________
GH
The order of the points in the similarity statements matter – they show which angles
are congruent and which segments are proportional!!!! In other words, it tells you the names
of the corresponding angles and the corresponding sides!
Similarity 2
Now, Try These:
Are the polygons similar? If not, tell why. If so, write a similarity statement.
A)
B)
E
A
8
6
12
9
x
F
10
K
J
N
O
105
G
x
B
C
15
Q
80
M
___: are all corresponding angles congruent?
___: are all sides proportional?
Similar – yes or no.
If no, why ____________________________
Similarity statement ____________________
C)
R
___: are all corresponding angles congruent?
___: are all sides proportional?
Similar – yes or no.
If no, why ___________________________
Similarity statement ___________________
A
D)
S
P
L
B
E
F
H
G
W
D
T
U
C
V
___: are all corresponding angles congruent?
___: are all sides proportional?
Similar – yes or no.
If no, why ____________________________
Similarity statement ____________________
___: are all corresponding angles congruent?
___: are all sides proportional?
Similar – yes or no.
If no, why ___________________________
Similarity statement ___________________
E) These pentagons are similar:
a) Write a similarity statement.
L
G
6
12
y
Y
z
10
b) Give the scale factor. *small to big
x
6
J
M
12
I
15
c) JX = _________
4
x
z
X
4
N
H
18
y
K
Similarity 2
AA Similarity Theorem: If two ___________ of one triangle are _____________ to two
____________ of another triangle, then the two triangles are __________.
Example 1: Tell whether the triangles are similar or not similar. If they are similar, write a
similarity statement.
F
A)
C
B)
100
100
C)
M
30
D
A
X
E
Z
50
A
B
B
Y
N
Yes
No
________________
E
B
Yes
No
________________
70
D
A
B)
80
20
D
70
C
C
B
Yes
No
__________________
Example 2: Find x and y.
X
Hint: Separate the two triangles, then write a proportion to
solve.
20
20 + y
24
x
8
C
Z
x
y
30
B
F
Yes
No
___________________
16
20
16
Y
E
40
F
30
A
D
C
Yes
No
________________
Now, Try These:
A)
E
30
Similarity 2
SSS Similarity Theorem: If _______________________ sides of two triangles are
proportional then the two triangles are __________.
SAS Similarity Theorem: If an ______ of one triangle is congruent to an ______ of another
triangle, and the _______ of the sides including these angles are ___________, the
triangles are __________.
Example 3: Which two triangles are similar?
C
21
A
F
15
9
5
E
9
7
G
3
H
5
D
B
7
I
Determine whether the 2 triangles shown are similar. If so, state the postulate or theorem that justifies your
answer (AA~, SSS~, or SAS~).
4.
R
5.
R
63
F
6
9
X
8
6
6
3
T
Yes No
___________________
Q
G
63
3
4
S
Z
4
2
W
Y
H
Yes
No
____________________