3.2 Proving Lines Parallel
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
