Day 6 Problems 22508

1
Day 6 Problems 2/25/08

• Determine whether the triangles are similar. If
  they are similar, write a similarity statement.
• 1. 2.
• Find the value of the variable.
• 3. 4.

Q
G
K
32
T
R
L
M
58
J
H
S
U
y
7
8
18
p
16
32
24
2
Showing Triangles are Similar SSS and SAS

• Side Side Side Similarity Theorem (SSS)
• If the corresponding sides of two triangles are
  proportional, then the triangles are similar.
• If FG GH HF, then ABC FGH.
• AB BC CA

A
F
B
C
G
H
3
Use the SSS Similarity Theorem

• Determine whether the triangles are similar. If
  they are similar, write a similarity statement
  and find the scale factor of Triangle B to
  Triangle A.
• Solution.
• By the SSS Similarity Theorem,
• PQR STU. The scale
• 
  factor of Triangle B to Triangle A
  is 1 .
• 2

P
S
12
8
A
6
4
B
Q
R
T
U
10
5
4
Use the SSS Similarity Theorem

• Is either DEF or GHJ similar to
  ABC?
• Solution.
• 1. Look at the ratios of corresponding sides in
  ABC and
• DEF.
• ABC DEF.

B
H
E
9
6
10
6
6
4
C
8
F
D
A
12
14
G
J


5
Use the SSS Similarity Theorem

• Is either DEF or GHJ similar to
  ABC?
• Solution.
• 2. Look at the ratios of corresponding sides in
  ABC and
• GHJ.
• ABC and GHJ are not similar.

A
H
E
9
6
10
6
6
4
C
8
F
D
B
12
14
G
J


6
SAS Similarity Theorem (SAS)

• Side-Angle-Side Similarity Theorem (SAS)
• If an angle of one triangle is congruent to an
  angle of a second triangle and the lengths of the
  sides that include these angles are proportional,
  then the triangles are similar.
• If X M and PM MN, then XYZ
  MNP.
• ZX XY

X
M
P
N
Y
Z


7
Use the SAS Similarity Theorem

• Determine whether the triangles are similar. If
  they are similar, write a similarity statement.
• Solution.
• B and F both measure 61, so B
  F.
• Compare the ratios of the side lengths that
  include B and F.
• The lengths of the sides that include
• 
  B and F are proportional.
• By the SAS Similarity Theorem, ABC
  DFE.

D
A
5
3
61
F
E
10
61
C
B
6

8
Similarity of Overlapping Triangles

• Show that VYZ VWX.
• Solution.
• V V by the Reflexive Property of
  Congruence.
• The lengths of the sides that include V are
  proportional.
• By the SAS Similarity Theorem, VYZ
  VWX.

V
5
4
X
W
8
10
Z
Y

9
More Practice!!!

• Textbook p. 382 383 6 18 even.