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

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Practice for Proofs of: Parallel Lines Proving Converse of AIA, AEA, SSI, SSE. By Mr. Erlin Tamalpais High School 10/20/09. r. Converse of Alternate Interior Angles Theorem. Given :. Statement Reason. 1. 2. p. 3. 4. 5. 6. Prove : p is parallel to q. q. 7. 8.

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

By Mr. Erlin

Tamalpais High School

10/20/09

r

Converse of Alternate Interior Angles Theorem

Given:

Statement Reason

1

2

p

3

4

5

6

Prove: p is parallel to q

q

7

8

& 4  5

• 4  5
• 4 & 5 are alt interior angles
• 1 & 4 are vertical angles
• 1  4
• 1  5
• 1 & 5 are Corresponding Angles
• r is a transversal over p, q
• p is parallel to q
• Given
• Given/Definition of AlA
• Definition of Vertical Angles
• If Vertical Angles, then 
• Transitive Prop 
• Definition of Corresponding Angles.
• Given/Definition of Transversal
• If lines cut by a transversal form corresponding angles that are , then lines are parallel

QED

r

Converse of Alternate Exterior Angles Theorem

Given:

Statement Reason

1

2

p

3

4

5

6

Prove: p is parallel to q

q

7

8

& 1  8

• Given
• Given/Definition of AEA
• Definition of Vertical Angles
• If Vertical Angles, then 
• Symmetric Prop 
• Transitive Prop of 
• Definition of Corresponding Angles.
• Given/Definition of Transversal
• If lines cut by a transversal form corresponding angles that are , then lines are parallel
• 1  8
• 1 & 8 are alt exterior angles
• 1 & 4 are vertical angles
• 1  4
• 4  1
• 4  8
• 4 & 8 are Corresponding Angles
• r is a transversal over p, q
• p is parallel to q

QED

Converse of Same Side Interior Angles are Supplementary

transversal

corresponding

congruent

lines are parallel.

r

Given:

Statement Reason

1

2

p

Prove: Line p is parallel to line q

3

4

5

6

q

and: 3 &5 are supplementary

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

QED

Converse of Same Side Exterior Angles are Supplementary

transversal

corresponding

congruent

lines are parallel.

r

Given:

Statement Reason

1

2

p

Prove: Line p is parallel to line q

3

4

5

6

q

7

and: 1 &7 are supplementary

• Given
• Given
• Definition of Supplementary
• Definition of Linear Pair
• If Linear Pair, then Supplementary
• Definition of Supplementary
• Substitution Prop. of Equality
• Subtraction Prop. of Equality
• Definition of Congruent Angles
• Definition of Corresponding s
• If then
• R is a transversal to P, Q
• 1 & 7 are Supplementary
• m1 + m7= 180
• 3 and 1 form a Linear Pair
• 3 & 1 are Supplementary
• m3 + m1 = 180
• m1 +m7 = m3 + m1
• m7=m3
• 73
• 7 & 3 are Corresponding s
• P is parallel to Q

QED