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Practice for Proofs of: Parallel Lines Proving AIA, AEA, SSI, SSE only. By Mr. Erlin Tamalpais High School 10/05/2010. Note: Blue slides match scaffolded notes handout. r. parallel transversal corresponding. angles are congruent. Given :. Alternate Interior Angles are .

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practice for proofs of parallel lines proving aia aea ssi sse only

Practice for Proofs of: Parallel LinesProving AIA, AEA, SSI, SSE only

By Mr. Erlin

Tamalpais High School

10/05/2010

Note: Blue slides match scaffolded notes handout

statement reason

r

parallel

transversal

corresponding

angles are congruent

Given:

Alternate Interior Angles are 

Statement Reason

1

2

p

3

4

Prove: 4  5

5

6

q

  • p is parallel to q
  • r is a transversal to p, q
  • 1 and 5 are Corresponding Angles
  • 1  5
  • 1 and 4 are Vertical Angles
  • 1  4
  • 4  1
  • 4  5
  • Given
  • Given
  • Definition of Corresponding Angles
  • If then
  • Definition of Vertical Angles
  • If Vertical Angles, then 
  • Symmetric Prop 
  • Transitive Prop 

QED

statement reason1

r

Given:

Alternate Interior Angles are 

Statement Reason

1

2

p

3

4

Prove: 4  5

5

6

q

  • p is parallel to q
  • r is a transversal to p, q
  • 1 and  ____ are Corresponding Angles
  • 1  5
  • ____ and 4 are Vertical Angles
  • ____________
  • 4  _______
  • ___________
  • Given
  • Given
  • Definition of _____________ Angles
  • If ______ then _______
  • Definition of ______ Angles
  • If Vertical Angles, then 
  • Symmetric Prop 
  • Transitive Prop 

QED

statement reason2

r

parallel

transversal

corresponding

angles are congruent

Given:

Alternate Interior Angles are 

Statement Reason

1

2

p

3

4

Prove: 4  5

5

6

q

  • p is parallel to q
  • r is a transversal to p, q
  • 1 and  ____ are Corresponding Angles
  • 1  5
  • ____ and 4 are Vertical Angles
  • ____________
  • 4  _______
  • ___________
  • Given
  • Given
  • Definition of _____________ Angles
  • If ______ then _______
  • Definition of ______ Angles
  • If Vertical Angles, then 
  • Symmetric Prop 
  • Transitive Prop 

5

Corresponding

1

Vertical

1  4

1

4 5

QED

statement reason3

t

Given:

Alternate Interior Angles are 

Statement Reason

2

l

3

Prove: 3  6

6

m

  • l is parallel to m
  • t is a transversal to l & m
  • 6 and  ____ are Corresponding Angles
  • 6  2
  • ____ and 3 are Vertical Angles
  • _____ ______
  • 6  _______
  • ___________
  • Given
  • Given
  • Definition of _____________ Angles
  • If ______ then _______
  • Definition of ______ Angles
  • If Vertical Angles, then 
  • Transitive Prop 
  • Symmetric Prop 

QED

statement reason4

t

parallel

transversal

corresponding

angles are congruent

Given:

Alternate Interior Angles are 

Statement Reason

2

l

3

Prove: 3  6

6

m

  • l is parallel to m
  • t is a transversal to l & m
  • 6 and  ____ are Corresponding Angles
  • 6  2
  • ____ and 3 are Vertical Angles
  • _____ ______
  • 6  _______
  • ___________
  • Given
  • Given
  • Definition of _____________ Angles
  • If ______ then _______
  • Definition of ______ Angles
  • If Vertical Angles, then 
  • Transitive Prop 
  • Symmetric Prop 

2

Corresponding

Vertical

2

2 3

3

3 6

QED

statement reason5

r

parallel

transversal

corresponding

angles are congruent

Alternate Exterior Angles are 

Given:

Statement Reason

1

2

p

3

4

Prove: 1  8

5

6

q

7

8

  • p is parallel to q
  • r is a transversal to p, q
  • 1 and 5 are Corresponding Angles
  • 1  5
  • 5 and 8 are Vertical Angles
  • 5  8
  • 1  8
  • Given
  • Given
  • Definition of Corresponding Angles
  • If then
  • Definition of Vertical Angles
  • If Vertical Angles, then 
  • Transitive Prop 

QED

statement reason6

r

Alternate Exterior Angles are 

Given:

Statement Reason

1

2

p

3

4

Prove: 1  8

5

6

q

7

8

  • p is parallel to q
  • r is a transversal to p, q
  • 1 and 5 are Corresponding Angles
  • 1  5
  • 5 and 8 are Vertical Angles
  • 5  8
  • 1  8
  • _________
  • _________
  • ________ of ____________ ________
  • If then
  • __________ of _________ _________
  • If ________, then ______
  • _____________________

QED

statement reason7

parallel

transversal

corresponding

angles are congruent

Same Side Interior Angles are Supplementary

r

Statement Reason

Given:

Prove:

3 &5 are supplementary

1

2

p

3

4

5

6

q

  • p is parallel to q
  • r is a transversal to p, q
  • 1 and 5 are Corresponding Angles
  • 1  5
  • 3 and 1 are Linear Pair
  • 3 & 1 are Supplementary
  • m3 + m1 = 180
  • m1 = m5
  • m3 + m5= 180
  • 3 & 5 are Supplementary
  • Given
  • Given
  • Definition of Corresponding Angles
  • If then
  • Definition of Linear Pair
  • If Linear Pair, then Supplementary
  • Definition of Supplementary (or if supplementary then 180)
  • Definition of Congruent Angles
  • Substitution Prop of Equality
  • Definition of Supplementary

QED

statement reason8

parallel

transversal

corresponding

angles are congruent

Same Side Interior Angles are Supplementary

r

Statement Reason

Given:

Prove:

3 &5 are supplementary

1

2

p

3

4

5

6

q

  • p is parallel to q
  • r is a __________ to p, q
  • 1 and 5 are _________________ Angles
  • ____  ____
  • 3 and 1 are ________
  • __ & __ are Supplementary
  • m3 + m1 = ______
  • m1 = m5
  • m3 + m5= 180
  • 3 & 5 are ___________
  • _________
  • Given
  • __________ of Corresponding Angles
  • If then
  • Definition of ____________
  • If Linear Pair, then ____________
  • __________ of Supplementary
  • Definition of Congruent Angles
  • __________ Prop of Equality
  • Definition of Supplementary

QED

statement reason9

Same Side Interior Angles are Supplementary

t

Statement Reason

Given:

Prove:

6 &4 are supplementary

2

l

4

m

6

  • l// m; t is a __________ to l & m
  • 6 & 2 are ___________ Angles
  • ____  ____
  • m6 = m2
  • 2 & 4 form ________
  • __ & __ are Supplementary
  • m2 + m4 = ______
  • m6 + m4= 180
  • 6 & 4 are ___________
  • _________
  • ______ of Corresponding Angles
  • If then
  • Definition of Congruent Angles
  • Definition of ____________
  • If Linear Pair, then ____________
  • __________ of Supplementary
  • __________ Prop of Equality
  • Definition of Supplementary

parallel

transversal

_________

angles are _________

QED

statement reason10

Same Side Interior Angles are Supplementary

t

Statement Reason

Given:

Prove:

6 &4 are supplementary

2

l

4

m

6

transversal

Given

  • l// m; t is a __________ to l & m
  • 6 & 2 are ___________ Angles
  • ____  ____
  • m6 = m2
  • 2 & 4 form ________
  • __ & __ are Supplementary
  • m2 + m4 = ______
  • m6 + m4= 180
  • 6 & 4 are ___________
  • _________
  • ______ of Corresponding Angles
  • If then
  • Definition of Congruent Angles
  • Definition of ____________
  • If Linear Pair, then ____________
  • __________ of Supplementary
  • __________ Prop of Equality
  • Definition of Supplementary

corresponding

Defin.

parallel

transversal

_________

angles are _________

congruent

6 2

corresponding

Linear Pair

Linear Pair

supplementary

2 4

180

Definition

Substitution

Supplementary

QED

statement reason11

parallel

transversal

corresponding

angles are congruent

Same Side Interior Angles are Supplementary

r

Statement Reason

Given:

Prove:

3 &5 are supplementary

1

2

p

3

4

5

6

q

  • ________________
  • ________________
  • 1 and 5 are ______________________
  • _______________
  • 3 and 1 are ___________
  • 3 & 1 are _____________
  • m3 + m1 = _______
  • m1 = m_____
  • ___________= 180
  • ______________________
  • Given
  • Given
  • Definition of Corresponding Angles
  • If then
  • Definition of Linear Pair
  • If Linear Pair, then Supplementary
  • Definition of Supplementary
  • Definition of Congruent Angles
  • Substitution Prop of Equality
  • Definition of Supplementary

QED