Given: HI = 9, IJ = 9, and IJ ≅ JH
Prove: HI ≅ JH
H
I
J
Statements
1. HI = 9
Reasons
1.
#1
2. IJ = 9
2.
#44
3. HI = IJ
3.
#30
4.
4. Definition of Congruent Segments
#39
5. IJ ≅ JH
5.
#68
6. HI ≅ JH
6.
#70
Given
Given
Substitution Property
W
W
A
Given
Transitive Property
HI ≅ IJ
W
E
A
Given:  3 and  2 are complementary, m  1+m  2 = 90o
Prove:  1 ≅  3
2
3
1
Statements
1.  3 and  2 are
Complementary
Reasons
1.
#2
2. m  1+m  2 = 90o
2.
#21
3. m  3+m  2 = 90o
3.
#56
4. m  1+m  2 = m  3+m  2 4.
#43
5. m  1 = m  3
5.
#66
6.  1 ≅  3
6.
#29
Given
Given
H
Definition of complementary Definition of congruent
angles
T angles
Substitution Property
Subtraction Property
E
H
R
A
Given: AL = SK
Prove AS = LK
A
L
S
Statements
1. AL = SK
Reasons
1.
#32
2. LS = LS
2.
#61
3. AL + LS = SK + LS
3.
#76
4. AL + LS = AS
4.
#7
5. SK + LS = LK
5.
#67
6. AS = LK
6.
#40
Given
Addition Property
Segment Addition Postulate
L
E
Y
K
Reflexive Property
Substitution Property
Segment Addition Postulate
C
N
Y
Given: m  4 = 120o,  2 ≅  5,  5 ≅  4
Prove: m  2 = 120o
6
5
1
4
2
3
Statements
1. m  4 = 120o,  2 ≅  5,
5≅ 4
Reasons
1.
#23
2.  2 ≅  4
2.
#50
3.
3. Definition of
Congruent Angles
#72
4. m  2 =120o
Given
Transitive Property
4.
T
D
#15
m 2 = m 4
Substitution Property
H
A
Given:  1 and  2 are complementary,  1 ≅  3,  2 ≅  4
Prove:  3 and  4 are complementary
1
Statements
1.
#59
Reasons
1. Given
2. m  1 + m  2 = 90o
2.
3.
3. Given
#24
2 34
#31
4. m  1 = m  3, m  2 = m  4 4.
#16
5. m  3 + m  4 = 90o
5.
#28
6.
6. Definition of
complementary angles
#75
 1 and  2 are
complementary
Substitution Property
Definition of Congruent
Angles
 3 and  4 are
E complementary
R
Definition of Complementary
O Angles
B
 1 ≅  3,  2 ≅  4
N
I
4
Given:  1 ≅  2
Prove:  3 ≅  4
Statements
1.
1
3
2
#55
Reasons
1.
#53
2.
#10
2.
#69
3.
#34
3.
#25
1≅ 2
 1 ≅  3,  2 ≅  4
Substitution Property
I
C
S
3≅ 4
Given
Vertical Angles Theorem
A
E
H
E
Given: m  CBE = m  ABD
Prove: m  CBD = m  ABE
D
C
A
B
Statements
1. m  CBE = m  ABD
Reasons
1.
#5
2. m  ABE = m  ABD + m  DBE
2.
#6
3. m  ABE = m  CBE + m  DBE
3.
#58
4. m  CBE + m  DBE = m  CBD
4.
#8
5. m  ABE = m  CBD
5.
#73
Angle Addition Postulate
Substitution Property
Given
O
L
D
Angle Addition Postulate
Transitive Property
O
E
Given: RT = SU
Prove: RS = TU
R
S
T
U
Statements
1. RT = SU
1.
Reasons
#49
2. ST = ST
2.
#36
3. RT – ST = SU – ST
3.
#18
4. RT – ST = RS
4.
#79
5.
5. Segment Addition Postulate
#26
6. RS = TU
Given
Segment Addition Postulate
Subtraction Property
6.
I
P
L
#63
Reflexive Property
Substitution Property
SU – ST = TU
U
R
A
A
Given: m  ABD = m  CBE
Prove: m  1 = m  3
B
1
2
3
C
D
E
Statements
1.
#51
Reasons
1. Given
2.
#48
2. Reflexive Property
3.
#77
3. Subtraction Property
4.
#17
4. Angle Addition Postulate
5. m  CBE - m  2 = m  3 5.
#41
6.
#62
6. m  1 = m  3
m  ABD - m  2 = m  CBE - m  ABD - m  2 = m  1
m 2
W
Angle Addition Postulate
Substitution Property
G
m  ABD = m  CBE
m 2 = m 2
T
G
O
D
Given: M is the midpoint of AB
N is the midpoint of CD
AB = CD
����� ≅ ����
Prove: 𝐴𝑀
𝐶𝑁
Statements
1. M is the midpoint of AB 1.
N is the midpoint of CD
A
M
B
C
N
D
Reasons
#3
2. AM = MB, CN = ND
2.
#42
3. AB = CD
3.
#14
4. AM + MB = AB,
CN + ND = CD
4.
#47
5. AM + AM = AB,
CN + CN = CD
5.
#4
6. 2AM = AB, 2CN = CD 6.
#74
7. 2AM = 2CN
7.
#20
8. AM = CN
8.
#33
9. �����
𝐴𝑀 ≅ ����
𝐶𝑁
9.
#60
Given
Substitution Property
A
Given
Substitution Property
T
Simplify/Combine Like Terms Division Property
G
Definition of a Midpoint
Definition of Congruent
L Segments
Segment Addition Postulate
T
A
T
E
A
1
Given: l ⊥ m, l ⊥ n
Prove:  1 ≅  2
l
m
n
2
Statements
1.
#19
Reasons
1.
#38
2.
#57
2.
#71
3.
#46
3.
#11
 1 and  2 are right angles
1≅ 2
l ⊥ m, l ⊥ n
All right angles are congruent
A
T
Given
E
A
Definition of Perpendicular
E Lines
N
Given:  2 ≅  3
Prove:  3 ≅  6
1
23
4
7 6 5
Statements
1.
#9
Reasons
1.
#22
2.
#54
2.
#35
3.
#45
3.
#65
2≅ 3
3≅ 6
2≅ 6
Vertical Angles Theorem
U
H
L
Given
Substitution Property
C
A
S
1
Given  1 ≅  5
Prove:  1 is supplementary to  4
2
3
4 5
Statements
1.
#64
Reasons
1. Given
2.
2. Definition of Congruent
Angles
#37
3.  4 and  5 are a
linear pair
3.
#52
4. m  4 and m  5 are
supplementary
4.
#78
5. m  4 + m  5 = 180o
5.
#12
6.
6. Substitution Property
#27
7.  1 is supplementary to
4
7.
#13
m 1 = m 5
1≅ 5
T
m  4 + m  1 = 180o
Supplement Theorem
D
U
N
Definition of Supplementary Definition of Supplementary
L
L
Assume from diagram
H
Names: ______________________________________________
1. ___ ___ ___ ___
1 2 3 4
___ ___ ___ ___
10 11 12 13
___ ___ ___ ___
20 21 22 23
___ ___ ___ ___ ___
26 27 28 29 30
___ ___
___ ___ ___
5 6
7 8 9
___ n
___ ___ ___ ___ ___
14
15 16 17 18 19
___ ___
24 25
___ ___ ___?
31 32 33
Answer: ___ ___ ___ ___ ___
34 35 36 37 38
2. ___ ___ ___ ___
44 45 46 47
___ ___ ___ ___ ___
54 55 56 57 58
___ ___ ___
___
65 66 67
68
___ ___ ___ ___
74 75 76 77
___ ___ ___ ___ ___
39 40 41 42 43
___ ___ ___
___ ___ ___
48 49 50
51 52 53
___
___ ___ ___ ___ ___
59
60 61 62 63 64
___ ___ ___
___ ___
69 70 71
72 73
___ ___ ?
78 79
Your answer: _________________________________________