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Lesson 3-3
Objective – To prove lines parallel.
Converse of Corresponding Angles Postulate
If two coplanar lines are cut by a transversal and
the corresponding angles are congruent, then the
lines are parallel.
Objective – To prove lines parallel.
Converse of Corresponding Angles Postulate
If two coplanar lines are cut by a transversal and
the corresponding angles are congruent, then the
lines are parallel.
Parallel Line Construction
Parallel Line Construction
C
C
B
B
A
A
Objective – To prove lines parallel.
Converse of Corresponding Angles Postulate
If two coplanar lines are cut by a transversal and
the corresponding angles are congruent, then the
lines are parallel.
Objective – To prove lines parallel.
Converse of Corresponding Angles Postulate
If two coplanar lines are cut by a transversal and
the corresponding angles are congruent, then the
lines are parallel.
Parallel Line Construction
Parallel Line Construction
D
C
C
B
B
A
A
Objective – To prove lines parallel.
Converse of Corresponding Angles Postulate
If two coplanar lines are cut by a transversal and
the corresponding angles are congruent, then the
lines are parallel.
Parallel Line Construction
 
AC  BD
B
A
Given: 2  3
Prove: a  b
Statement
D
C
Converse of the Alternate Interior Angles Theorem
If two coplanar lines are cut by a transversal and
the alternate interior angles are congruent, then
the lines are parallel.
- Construct
congruent
angles
1) 2  3
2) 1  2
3) 1  3
4) a  b
1
3
2
a
b
Reasons
Given
Vertical Angles Thm.
Transitive Prop of Cong.
Conv. of Corres. s Post.
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014
1
Lesson 3-3
Converse of the Same Side Interior Angles Theorem
Converse of
If two lines are cut by a transversal
Alt. Int. Angles - and the alt. int. angles are congruent
Theorem
then the lines are parallel.
Prove: If 2 & 3 are suppl., then a  b.
Statement
Converse of
If two lines are cut by a transversal
Alt. Ext. Angles -and the alt. ext. angles are congruent
Theorem
then the lines are parallel.
Converse of
If two lines are cut by a transversal
SS. Int. Angles - and the SS. int. angles are suppl.
Theorem
then the lines are parallel.
c
d
a
1 2
3 4
5 6
7 8
1) 2 & 3 are suppl.
2)) 1 & 2 are linear ppair.
3) 1 & 2 are suppl.
4) 1  3
5) a  b
9 10
11 12
c
13 14
15 16
b
1 2
a
d
a
1 2
3 4
5 6
7 8
3
b
Reasons
Given
Def. of linear p
pair
Linear Pair Theorem
 Suppl. Thm.
Conv. of Corres. s Post.
9 10
11 12
13 14
15 16
b
Which lines are proved parallel by the following, why?
Which lines are proved parallel by the following, why?
1) 11  15
4) 12  16
c  d ,Conv.
c  d ,Conv.
Conv Corres.
Corres
Conv Corres.
Corres
s Post.
s Post.
2) 5  16
5) 5  13
a  b ,Conv. Alt. Ext.
a  b ,Conv. Corres.
s Thm.
s Post.
3) 4  9
6) 6 suppl. to 13
a  b ,Conv. Alt. Int.
a  b ,Conv. SS. Int.
s Thm.
s Thm.
7) 7  3
10) 8  16
c  d ,Conv.
a  b ,Conv.
Conv Corres.
Corres
Conv Corres.
Corres
s Post.
s Post.
11) 10  15
8) 11  14
c  d ,Conv. Alt. Int.
c  d ,Conv. Alt. Ext.
s Thm.
s Thm.
12) 13  16
9) 4  13
No conclusion
No conclusion
Prove a  b given the
following information.
5 6
7 8
1 2
3 4
a
1) m2  m7
2  7 , Def.  s
a  b , Conv. Alt. Int. s Thm.
b
2) m1  3x
3  10,
10 m8  5x
5  40,
40 x  25
m1  3(25)  10  85 , Substitution
m8  5(25)  40  85
m1  m8 , Substitution
1  8 , Def.  s
a  b , Conv. Alt. Ext. s Thm.
Prove a  b given the
following information.
5 6
7 8
1 2
3 4
a
b
3) m1  m7  180
1  4 , Vert. s Thm.
m1  m4 , Def.  s
S b tit ti
m4  m7  180 , Substitution
m4 & m7 are suppl. , Def. Suppl. s
a  b , Conv. SS. Int. s Thm.
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014
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