3.2 Proving Lines Parallel

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3.2 Proving Lines Parallel

-Alfred Borden

Proving Lines Parallel l m

2

1

Postulate 3-2: Converse of Corresponding Angles Postulate:

If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel.

l

||

m



Proving Lines Parallel

We know these two lines are parallel!!

If Alternate Interior Angles are congruent we can assume lines are parallel too!

Proving Lines Parallel l m

1 4

2

Theorem 3-5: Converse of Alternate Interior Angles Theorem

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

If

1

 

2, then

l

||

m

.



Proof of Theorem 3-5 (C of AIAT)









Given :  2   1

Prove : l || m l m

1.

Statements

 2   1

2.

3.

4.

 2   3 l

||

m



1

2

3

Reasons

1.

2.

Vertical  's are 

3.

4.

Proving Lines Parallel

We know these two lines are parallel!!

If Same-Side Interior Angles are supplementary, we can assume lines are parallel too!!

Proving Lines Parallel l m

1 4

2

Theorem 3-6: Converse of Same-Side Interior Angles Theorem

If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel.

If

2 and

4 are supplement ary, then

l

||

m

.

Proving Lines Parallel

We know these two lines are parallel!!

If Alternate Exterior Angles are congruent, we can assume lines are parallel!!!

Proving Lines Parallel a b

1

3 2

Theorem 3-7: Converse of Alternate Exterior Angles Theorem

If two lines and a transversal intersects form alternate exterior angles that are congruent, then the two lines are parallel.

If

1

 

2 , then

a

||

b

.

Proof of Theorem 3-7 (C of AEAT)









Given :  2   1

Prove : a || b a b

1

4

2

Statements

1.

2.

3.

4.

 1   4

 2   4 a

||

b

2.

3.

Reasons

1.

4.

Proving Lines Parallel

We know these two lines are parallel!!

If Same-Side Exterior Angles are supplementary, we can assume lines are parallel!!!



Proving Lines Parallel a b

1

3 2

Theorem 3-8: Converse of Same-Side Exterior Angles Theorem

If two lines and a transversal intersects form same-side exterior angles that are supplementary, then the two lines are parallel.

If

1 and

3 are supplementary, then

a

||

b

.

Let’s Apply What We Have Learned, K?

Find the value of x for which l || m l m

40

°

(2 x + 6)

°

You Try One!

Find the value of x for which a || b a b

(7 x - 8)

°

62

°

3.2: Proving Lines Parallel

Homework 3.2:

#1-8, 14-22, 24-

30 even

-Forrest

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