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

1 / 13

# Practice for Proofs of: Parallel Lines Proving AIA, AEA, SSI, SSE only - PowerPoint PPT Presentation

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 .

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## Practice for Proofs of: Parallel Lines Proving AIA, AEA, SSI, SSE only

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 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

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

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

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

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

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

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

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

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

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

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

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

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