Proofs Parallel Lines 2

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Proofs Parallel Lines 2

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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