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T
V
Given: <V ≅ <YRX
<Y ≅ <TRV
Prove: <V ≅ <Y
R
Y
**Two Column Proof
WARM UP
X
T
V
Given: <V ≅ <YRX
<Y ≅ <TRV
Prove: <V ≅ <Y
R
Y
Statements
Reasons
1. <V ≅ <YRX
<Y ≅ <TRV
1. Given
2. <TRV and <YRX are vertical
<s.
2. Assumed from diagram
3.<TRV ≅ <YRX
3. Vertical <s are ≅
4. <V ≅ <Y
4. Transitive Property
THE ANSWER!!
X
Advanced Geometry
Section 5.2 Proving lines are parallel

If two lines are cut by a transversal such
that two alternate interior angles are
congruent, then the lines are parallel.

's


Shortcut: Alt int 
|| lines

1
2
Theorem
l
m
1
2
,then l ||m.
If 

Alt ext

's


|| lines
1
8
Theorem
l
m
1
8
,
If 
then l || m.

's


Corresp 
|| lines
1
5
Theorem
l
If

1
5
,
then l || m.
m
If two lines are cut by a transversal such
that two interior angles on the same
side of the transversal are
supplementary, then the lines are
parallel.
 Same side int ' s suppl || lines



3
5
Theorem
a
b

3

m

5

18
,
If m
then a|| b.
Same side ext <‘s supp => || lines.
1
7
Theorem
a
b
1
and

7
If 
are supp,
then a||b.

If two coplanar lines are
then they are ||.
a
b
c
Theorem

to a 3rd line,
If a c and b  c,
then a|| b.

Read Sample Problem 1 on p. 218

Homework: p. 220 #4, 5, 8, 9, 13, 16,
20, 21, 24
**TEST Next Tuesday
Index Cards due, too!!! (50)
Homework