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Geometry
3.2 Properties of Parallel Lines
Postulate

If two // lines are cut by a transversal, then
corresponding angles are congruent.
~
// Lines => corr. <‘s =
2
1
4
3
5
7
6
8
Example: <1 =~ <5
Theorem

If two // lines are cut by a transversal, then
alternate interior angles are congruent.
~
// Lines => alt int <‘s =
2
1
4
3
5
7
6
8
Example: <3 =~ <6
We can prove this theorem using the previous postulate.
Theorem

If two // lines are cut by a transversal, then same
side interior angles are supplementary.
// Lines => SS Int <‘s supp
2
1
4
3
5
7
6
8
Example: <4 is supp to <6
Planning Its Proof

If two // lines are cut by a transversal, then same
side interior angles are supplementary.
Given: k // n
Prove: <1 is supp to <4
k
1
4
2
n
Theorem

If a transversal is perpendicular to one of
two parallel lines, then it is perpendicular
to the other line.
Planning Its Proof

If a transversal is perpendicular to one of
two parallel lines, then it is perpendicular
to the other line.
Given: k // n; t
Prove: t
n
k
t
1
k
2
n
Why is…
~ <4?
…<5 =
~
// Lines => alt int <‘s =
…<8 ~
= <4?
~
// Lines => corr. <‘s =
…<5 supp to <3?
…j
t, if k
t?
// Lines => SS Int <‘s supp
If a transversal is perp. to 1 of 2 // lines, it is perp. to both.
t
2
1
4
3
5
7
6
8
k
j
Let’s do some from the HW
together!

Page 81-82 #11, #16, #18

HW Page 80-82 CE #2-9, WE 1-15 Odd,
18-21