4.1 4.2 Congruency

1
4.1 4.2Congruency
2

• Congruency
• Congruent figures ____________________________
• __________________________________________
• __________________________________________________
  __________________________________________________
  __________________________

Angles Sides
D
A
B
C
E
F
3
In a proof, if triangles are congruent and you
plan to prove that corresponding pieces are
congruent use __ __ __ __
__ __________________________________________ ___
_______________________________________ __________
________________________________ _________________
_________________________
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Reasons for Proving Triangles Congruent Postulate
12 ____________________________ ________________
__________________________ _______________________
___________________ ______________________________
____________
5
Postulate 13 _____________________________ _____
___________________________________ ______________
__________________________ _______________________
_________________ ________________________________
________
6
Postulate 14_______________________________ _____
_____________________________________ ____________
______________________________ ___________________
_______________________ __________________________
________________
7
O
T
M
K
8
A
Z
Y
1
2
4
3
B
9
4.3 Proving other Congruencies
10
M
1
3
K
J
2
4
O
11
C
D
1
2
B
A
12
C
B
D
A
13
M
k
J
1
2
4
3
L
14
M
k
J
1
2
4
3
L
15
R
S
O
P
Q
16
B
A
E
C
D
17
4.4 Isosceles Triangles
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Lets draw an Isosceles Triangle
19

• Def of Isosceles Triangle
• _______________________________________

Theorem 4-1 ___________________________________
_________________________________________________
_ ________________________________________________
__ _______________________________________________
___ Theorem 4-2________________________________
___________________________________________ ______
__________________________________________________
______________________________
20
Corollary 2 _________________________________ ___
_______________________________________ __________
________________________________ _________________
_________________________
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Examples
x
4x-6
16
50
18
X_______
X_______
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4.5 Triangles Congruent
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More Ways to Prove Triangles Congruent
Theorem 4.3_______________________________ ______
____________________________________ _____________
_____________________________ ____________________
______________________
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Theorem 4.4_______________________________ ______
____________________________________ _____________
_____________________________ ____________________
______________________ ___________________________
_______________
25
Examples
x
21
21
4x-1
3x3
65
19-x
X_______
X_______
26
L
P
x
Q
1
4
2
3
70
N
M
X________
27
Z
Y
A
B C
28
4.6 Proving More than one set of Triangles
Congruent
29
D
O
C
A
B
30
D
O
X
C
A
B
31
X
D
C
1
2
A
B
O
32
4.7 Altitude, Median and Perpendicular
Bisector
33

• Median ________________________________
• _________________________________________
• _________________________________________
• ___________________________________

A
C
B
34

• Altitude ____________________________
• _____________________________________
• ____________________________________
• Acute Right Obtuse

35
Perpendicular Bisector ___________________
________________________________________ ________
________________________________ _________________
_______________________ __________________________
_____________
36
PBT ___________________________________ _________
_______________________________ __________________
______________________ ___________________________
_____________
C
A
B
37
CPBT _________________________________ __________
______________________________ ___________________
_____________________ ____________________________
____________
C
A
B
38
Theorem 4.7 _______________________ _____________
________________________ _________________________
____________ _____________________________________
39
D
O
C
B
40
D
O
C
B