Download 3.5 Properties of Parallel Lines

3.5 Properties of Parallel Lines
Geometry Quiz 3.4
1. m1  90
; m2  90  1___ 2.
2. If two lines intersect to form a pair of adjacent congruent
angles, the lines are _______________.
11) 
13) Given; Given; + Prop. of =; + Prop. of =;
Transitive Prop. of =; Segment Addition Post.
15) In Class
17) 3.  + Post.; 4. Transitive Prop. of =; 5. Substitution
19) 1 and 2 are right 's because  lines form right 's.
Because 1 and 2 are right 's, m1  m2  90 .
1  2 because m1  m2.
2
5
21) m1  , m2  
5
2
9)
m1 m2  1 l1  l2
23) Yes
24) No
25) Not enough information.
26) Yes
A
C
O
B
D
3.5 Properties of Parallel Lines
Goal 1: How to identify 's formed by two lines
and a transversal.
Goal 2: How to use properties of
lines.
Power Standard #11
Apply skills of conjecture, analysis, and counter-example
to formulate a hypothesis and test it. (3.2.1)
[2.4-2.6, 3.3-3.6, 4.3, 4.4, 6.4, 8.5]
Corresponding Angles Postulate
2
1
If two parallel lines are cut by a transversal,
then the pairs of corresponding angles are
congruent.
Corresponding Angles Postulate
2
1
If two parallel lines are cut by a transversal,
then the pairs of corresponding angles are
congruent.
Alternate Interior Angles Theorem
2
1
If two parallel lines are cut by a transversal,
then the pairs of alternate interior angles are
congruent.
Consecutive Interior Angles Theorem
2
1
If two parallel lines are cut by a transversal,
then the pairs of consecutive interior angles are
supplementary.
3.5 Properties of Parallel Lines
How is 9 related to the other 's?
9 and 10 are a linear pair
4 1
9 and 12 are a linear pair
9 and 11 are vertical 's
3 2
9 and 7 are alternate exterior 's
9 and 3 are alternate exterior 's
9 and 5 are corresponding 's
9 and 1 are corresponding 's
10
11 9
12
8
7 5
6
Alternate Exterior Angles Theorem
2
1
If two parallel lines are cut by a transversal, then
the pairs of alternate exterior angles are
congruent.
Perpendicular Transversal Theorem
If a transversal is perpendicular to one of two
parallel lines, then it is perpendicular to the
second.
3.5 Properties of Parallel Lines
Given : l1 l2 Prove: 3  5
Statements Reasons
t1 t2
Light enters
l1
1. Given
2. t1 t2
2. Given
3. 3  4 3.
4. 4  5 4.
3
5. 3  5
Glass
l2
1. l1 l2
5
4
Light exits t2
t1
lines  AEA's 
lines  CA's 
5. Transitive Prop.
3.5 Properties of Parallel Lines
HW 3.5/11-23 odd, 31-33