4'2 Congruence and Triangles

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4.2 Congruence and Triangles

• p. 202

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Congruent Figures
(
B
A
___

• 2 figures are congruent if they have the exact
  same size and shape.
• When 2 figures are congruent the corresponding
  parts are congruent. (angles and sides)
• Quad ABDC is congruent to Quad EFHG

___ ___
___ ___ ___
))))
___ ___ ___ ___
)))
((
D
C
F
(
E
___
___ ___ ___
___ ___
))))
___ ___ ___ ___
)))
((
H
G
3
?Z

• If ? ABC is ? to ? XYZ, which angle is ? to ?C?

4
Thm 4.33rd angles thm

• If 2 ?s of one ? are ? to 2 ?s of another ?, then
  the 3rd ?s are also ?.

5
Ex find x
)
)
22o
))
87o
))
(4x15)o
6
Ex continued

• 22874x15180
• 4x1571
• 4x56
• x14

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Ex ABCD is ? to HGFE, find x and y.
9cm
A
B
E
F
91o
(5y-12)o
86o
113o
D
C
H
G
4x-3cm
4x-39 5y-12113 4x12
5y125 x3
y25
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Thm 4.4Props. of ? ?s
A

• Reflexive prop of ? ? - Every ? is ? to itself
  (?ABC ? ?ABC).
• Symmetric prop of ? ? - If ?ABC ? ?PQR, then
  ?PQR ? ?ABC.
• Transitive prop of ? ? - If ?ABC ? ?PQR ?PQR ?
  ?XYZ, then ?ABC ? ?XYZ.

B
C
P
Q
R
X
Y
Z
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Given seg RP ? seg MN, seg PQ ? seg NQ , seg RQ
? seg MQ, m?P92o and m?N is 92o.Prove ?RQP ?
?MQN
N
R
92o
Q
92o
P
M
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• Statements Reasons
• 1. 1. given
• 2. m?Pm?N 2. subst. prop
• 3. ?P ? ?N 3. def of ? ?s
• 4. ?RQP ? ?MQN 4. vert ?s thm
• 5. ?R ? ?M 5. 3rd ?s thm
• 6. ?RQP ? ? MQN 6. def of ? ?s

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Assignment