Transcript Geometry

Geometry
3.1 Lines and Transversals
Parallel Lines // Lines
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Coplanar lines that do not intersect
k
j
j // k
Skew Lines
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Noncoplanar lines that do not intersect
h
g
line g is skew to line h
g and h are skew lines
// and Skew Lines
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What are some // lines in the diagram?
B
F
E
A
G
H
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C
D
What are some skew lines in the diagram?
Segments and rays…
…contained in // lines are also parallel.
.
.
A
AB // CD
.
B
.
C
AB // CD
D
Are segments QP and RS parallel?
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They do not intersect!
P
Q
R
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S
But they are parts of lines PQ and RS, which
are not parallel..
Thus, the answer is no!
// Planes…do not intersect
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What are some parallel planes in the diagram?
B
F
E
A
G
H
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C
D
Example: Plane ABCD // Plane EFGH
A line and a plane are // if they do not intersect!
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Examples?
B
F
E
A
G
H
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Example: Plane ABCD // EF
C
D
Theorem
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If two parallel planes are cut by a third plane,
then the lines of intersection are parallel.
j
k
j // k
Transversal

A line that intersects two or more coplanar
lines in different points.
t
t is a transversal
The lines do not need to be parallel to have a transversal !
Interior Angles and Exterior Angles
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Exterior angles 1, 2, 7, and 8.
Interior angles 3, 4, 5, and 6.
t
1
3
5
7
2
4
6
8
The lines do not need to be parallel for this to be true!
Alternate Interior Angles(Alt. Int <‘s)

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Two nonadjacent interior angles on opposite
sides of the transversal.
What are the two pairs of Alt. Int. <‘s?
t
1
3
5
7
2
4
6
8
<3 and <6
<4 and <5
The lines do not need to be parallel for this to be true!
Same Side Interior Angles(S.S. Int <‘s)

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Two interior angles on the same side of the
transversal.
What are the two pairs of S.S. Int. <‘s?
t
1
3
5
7
2
4
6
8
<3 and <5
<4 and <6
The lines do not need to be parallel for this to be true!
Corresponding Angles(Corr. <‘s)

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Two angles in corresponding positions
relative to the two lines.
What are the four pairs of Corr. <‘s?
t
1
3
5
7
2
4
6
8
<1 and <5
<3 and <7
<2 and <6
<4 and <8
The lines do not need to be parallel for this to be true!
Finding a transversal
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Trace each < identified.
The line you touch twice is the transversal.
Name the two lines and the transversal between angles…It helps to
draw an isolated picture
B
D
2
Angles 1 and 5
Transversal AE
Angles 2 and 6
1
A
3
F
E
4
5
6
C
7
8
Transversal BC
Angles 4 and 7
Transversal EF
Sometimes, Always, or Never?
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When there is a transversal of 2 lines, the 3
lines are _________ coplanar.
Answer: Always
2 Lines that are not coplanar __________
intersect.
Answer: Never
2 Planes // to the same line are _________ //
to each other.
Answer: Sometimes
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Review Sheet
Please open your books to page 76
#4, 6, 12, 18, 24, 26, 34, 38
4) Alt. Int <‘s
6) Corr. <‘s
8) Lines PS, QR, and transversal SQ
12) Corr. <‘s
18) Corr. <‘s are congruent
24) GH, ED, KJ
26) CDJI and GHIJKL
34) Sometimes
38) Sometimes
HW
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P. 76 – 77, #1-41 odd, skip 19 and 21
Self Test P. 65 Odds
Vocab Quiz tomorrow, Chapter 2 Test Friday
Ch. Review Today