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Proofs Parallel Lines 2
Contributed by: Pappal
Please complete the following proof
Which should be statement #1?
a
Given: ∡2 ≅ ∡7
Prove: a⇈b
b
1
3
2
4
5
7
6
8
c
1
Statements
∡2 ≅ ∡7

a⇈b

c⇈a

∡2 ≅ ∡3

Reasons
1
Which should be reason #1?
a
Given: ∡2 ≅ ∡7
Prove: a⇈b
b
1
3
2
4
5
7
6
8
c
1
∡2 ≅ ∡7
Statements

transitive

reflexive

given

alternate interior ∡

Reasons
1
Which should be statement #2?
a
Given: ∡2 ≅ ∡7
Prove: a⇈b
b
1
3
2
4
5
7
6
8
c
1

2

∡2 ≅ ∡7
Statements

∡2 ≅ ∡8

∡1 ≅ ∡4

∡2 ≅ ∡3

a⇈b

Reasons

2

1
given
Which should be reason #2?
a
Given: ∡2 ≅ ∡7
Prove: a⇈b
b
1
3
2
4
5
7
6
8
c
1

2

∡2 ≅ ∡7
Statements
∡2 ≅ ∡3

vertical

transitive

alternate interior ∡

corresponding ∡

Reasons

2

1
given
Which should be statement #3?
a
Given: ∡2 ≅ ∡7
Prove: a⇈b
b
1
3
2
4
5
7
6
8
c
1

2

3

∡2 ≅ ∡7
Statements
∡2 ≅ ∡3
∡7 ≅ ∡3

∡5 ≅ ∡8

a⇈b

∡3 ≅ ∡5

Reasons

2

3

1
vertical ∡
given
Which should be reason #3?
a
Given: ∡2 ≅ ∡7
Prove: a⇈b
b
1
3
2
4
5
7
6
8
c
1

2

3

∡2 ≅ ∡7
Statements
∡7 ≅ ∡3
∡2 ≅ ∡3

corresponding ∡

vertical ∡

transitive

reflexive

Reasons

2

3

1
vertical ∡
given
Which should be statement #4?
a
Given: ∡2 ≅ ∡7
Prove: a⇈b
b
1
3
2
4
5
7
6
8
c
1

2

3

4

∡2 ≅ ∡7
Statements
∡7 ≅ ∡3
∡2 ≅ ∡3

c⇈a

∡3 ≅ ∡5

a⇈b

∡5 ≅ ∡8

Reasons

2

3

4

1
vertical ∡
transitive
given
Which should be reason #4?
a
Given: ∡2 ≅ ∡7
Prove: a⇈b
b
1
3
2
4
5
7
6
8
c
1

2

3

4

∡2 ≅ ∡7
Statements
∡7 ≅ ∡3
∡2 ≅ ∡3
a⇈b

CPCTC

alternate interior ∡

corresponding ∡

transitive

Reasons

2

3

4

1
vertical ∡
transitive
given
Please complete the following proof
a
Given: ∡1 ≅ ∡8
Prove: a⇈b
b
Match the reasons with the correct statements
1
3
2
4
5
7
6
8
c
1

2

3

4

∡1 ≅ ∡8
Statements
∡1 ≅ ∡5
∡8 ≅ ∡5
a⇈b
Reasons

2

3

4

1
corresponding ∡
?
vertical ∡
?
transitive
?
given
?
Please complete the following proof
a
Given: ∡1 ≅ ∡8
Prove: a⇈b
b
Match the statements with the correct reason
1
3
2
4
5
7
6
8
c
1

2

3

4

∡1 ≅ ∡4
∡1 ≅ ∡8
?
Statements
∡8 ≅ ∡5
?
∡4 ≅ ∡5
?
a⇈b
?
Reasons

2

1

3

4

vertical ∡

alt int ∡

given

substitution

Please complete the following proof
a
Given: ∡2 ≅ ∡7
Prove: a⇈b
b
Match the statements with the correct reason
1
3
2
4
5
7
6
8
c
1

2

3

4

∡7 ≅ ∡6
?
∡2 ≅ ∡7
Statements
∡2 ≅ ∡3
∡3 ≅ ∡6
a⇈b
?
Reasons

2

1

3

4

vertical ∡

alt int ∡

given
?

substitution

?
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