Chapter 4 Congruent Triangles

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Chapter 4Congruent Triangles

• Sec. 4 1
• Congruent Figures

Objective 1) To recognize ? figures their
corresponding parts
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Congruent Polygons

• Are the same size and the same shape.
• Fit exactly on top of each other
• Have ? corresponding parts
• Matching sides and ?s

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You can make 3 kinds of moves so that one
congruent figure can fit exactly on top of top
of another
turn
slide
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You can make 3 kinds of moves so that one
congruent figure can fit exactly on top of top
of another
flip
flip
These are called translations and are covered in
chapter 9
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You can make 3 kinds of moves so that one
congruent figure can fit exactly on top of top
of another
slide
6
turn
7
flip
flip
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?QXT ? ?PHD
Means you can list the
corresponding parts without a diagram
QX ? PH
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Naming Polygons
When naming, always list cooresponding
points in order

• Order Matters!!

C
B
T
U
AB ? ED ? ?B ? ?D ? ?A ?
WU RS ?U ?S ?W
A
W
R
S
E
D
ABCDE ?
WUTSR
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Example ?WYS ? ?MKV

• m?W 25
• m?Y 55
• Find m?V

K
Y
55
M
V
25
W
100
S
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Example 2 Congruence Statement
Finish the following congruence statement ?JKL
? ?_ _ _
M
J
?JKL ?
?NML
L
K
N
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Proof Th(4-1)

• If 2 ?s of one ? are ? to 2 ?s another ?, then
  the third ?s are also ?.
• Given ?B ? ?E
• ?A ? ?D
• Prove ?C ? ?F

A
B
C
D
F
E
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• Statements
• ?B ? ?E ?A ? ?D
• m?B m?A m?C 180
• m?E m?D m?F 180
• 3) m?B m?A m?C
• m?E m?D m?F
• m?B m?A m?C
• m?B m?A m?F
• m?C m?F
• ?C ? ?F

• Reasons
• Given
• Def. of ?
• Trans.
• 4) Subs.
• Subtr.
• Def. of ?

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Example

• Proof
• Given GC ? GD
• CN ? DN
• Prove ?GCN ? ?GDN

G
D
C
N
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G
Show all of the parts are ?
given
3 sides
given
reflexive
D
C
N
given
3 angles
given
Thm 4-1