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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 lines proving converse of aia aea ssi sse

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

By Mr. Erlin

Tamalpais High School

10/20/09

statement reason

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

statement reason1

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

statement reason2

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

statement reason3

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