Download Ch 3-1 Parallel Lines and Transversals

Parallel Lines and
Transversals
Chapter 3-1
• Identify the relationships between two lines or two planes.
• Name angles formed by a pair of lines and a transversal.
• parallel lines
• consecutive interior angles
• parallel planes
• alternate exterior angles
• skew lines
• alternate interior angles
• transversal
• corresponding angles
Preparation for Standard 7.0 Students prove and use
theorems involving the properties of parallel lines cut by
a transversal, the properties of quadrilaterals, and the
properties of circles. (Key)
Parallel Lines
//
• Two lines are // if they are coplanar and do
not intersect.
Triangles are
used to indicate
// lines
Skew Lines
• Lines that do not intersect but are not
coplanar are called skew lines.
Parallel Planes
• Two planes that do not intersect.
Based on looks, find a line:
1.
2.
3.
4.
// to AB and containing D
 to AB and containing D
Skew to AB and containing D
Name the plane(s) that contain D and appear to
be // to plane ABE
C 1. DC
B
2. AD D
A
F
E
3. DH
H
4. DCH or DGH or DCG
G
Identify Relationships
A. Name all planes that are parallel to plane AEF.
Answer: plane BHG
Identify Relationships
__
B. Name all segments that intersect AF.
__ __ __
__
Answer: EF, GF, DA, and BA
Identify Relationships
__
C. Name all segments that are skew to AD.
__ __ __ __
__
Answer: FG, GB, EH, EC, and CH
A. Name a plane that is parallel
to plane RST.
A. plane
A
WTZ
B. plane
B
SYZ
D. plane
D
QRX
0%
0%
D
0%
C
A
0%
B
C. plane
C
WXY
B. Name a segment that
intersects YZ.
A. XY
B. WX
C. QW
0%
D
0%
C
A
D. RS
0%
B
0%
C. Name a segment that
is parallel to RX.
A. ZW
B. TZ
C. QR
0%
0%
0%
0%
D
C
B
A
D. ST
D. Name a segment
that
__
is skew to TZ.
__
A. RX
A
__
B. ST
B
0%
0%
D
0%
C
A
___
D. QW
D
0%
B
___
C. XW
C
Transversal
• A line that intersects two or more coplanar
lines at different points.
t
1 2
3 4
5 6
7 8
t is a transversal
Identify Transversals
A. BUS STATION Some of a bus station’s
driveways are shown. Identify the sets of
lines to which line v is a transversal.
Answer:
If the lines are extended, line v
intersects lines u, w, x, and z.
Identify Transversals
B. BUS STATION Some of a bus station’s
driveways are shown. Identify the sets of
lines to which line y is a transversal.
Answer:
lines u, w, x, z
Identify Transversals
C. BUS STATION Some of a bus station’s
driveways are shown. Identify the sets of
lines to which line u is a transversal.
Answer:
lines v, x, y, z
A. HIKING A group of nature trails is shown.
Identify the sets of lines to which line a is a
transversal.
A. lines
A c, f
B. lines
B c, d, e
C. lines
C c, d, f
D. lines
D c, d, e, f
0%
D
0%
C
0%
B
A
0%
B. HIKING A group of nature trails is shown.
Identify the sets of lines to which line b is a
transversal.
A. no
A lines
B. lines
B c, f
C. lines
C c, d, e, f
D. lines
D a, c, d, e, f
0%
D
0%
C
0%
B
A
0%
C. HIKING A group of nature trails is shown.
Identify the sets of lines to which line c is a
transversal.
A. lines
A a, b
B. lines
B a, b, d, e, f
C. lines
C a, d, f
D. lines
D a, b, e
0%
D
0%
C
0%
B
A
0%
D. HIKING A group of nature trails is shown.
Identify the sets of lines to which line d is a
transversal.
A. lines
A e, f
B. lines
B a, b, f
C. lines
C a, b, c, e, f
D. lines
D a, b, c
0%
D
0%
C
0%
B
A
0%
Corresponding Angles
• Two angles that occupy corresponding
positions.
1 and 5 are corresponding s
t
1 2
3 4
5 6
7 8
2 and 6 are corresponding s
3 and 7 are corresponding s
4 and 8 are corresponding s
Alternate Interior Angles
• Two angles that lie between the two lines on
opposite sides of the transversal.
t
1 2
3 4
5 6
7 8
3 and 6 are Alt. Int. s
4 and 5 are Alt. Int. s
Alternate Exterior Angles
• Two angles that lie outside the two lines on
opposite sides of the transversal.
t
1 2
3 4
5 6
7 8
1 and 8 are Alt. Ext. s
2 and 7 are Alt. Ext. s
Consecutive Interior Angles
• Two angles that lie between the two lines on
the same side of the transversal.
t
1 2
3 4
5 6
7 8
3 and 5 are Consecutive Int. s
4 and 6 are Consecutive Int. s
Sometimes
called Same
Side Interior
Angles
Identify Angle Relationships
A. Identify 7 and 3 as alternate interior, alternate
exterior, corresponding, or consecutive interior
angles.
Answer:
corresponding
Identify Angle Relationships
B. Identify 8 and 2 as alternate interior, alternate
exterior, corresponding, or consecutive interior
angles.
Answer:
alternate exterior
Identify Angle Relationships
C. Identify 4 and 11 as alternate interior, alternate
exterior, corresponding, or consecutive interior
angles.
Answer:
corresponding
Identify Angle Relationships
D. Identify 7 and 1 as alternate interior, alternate
exterior, corresponding, or consecutive interior
angles.
Answer:
alternate exterior
Identify Angle Relationships
E. Identify 3 and 9 as alternate interior, alternate
exterior, corresponding, or consecutive interior
angles.
Answer:
alternate interior
Identify Angle Relationships
F. Identify 7 and 10 as alternate interior, alternate
exterior, corresponding, or consecutive interior
angles.
Answer:
consecutive interior
A. Identify
4 and
5.
A. alternate
A
interior
B. alternate
B
exterior
C. corresponding
C
0%
D
0%
C
0%
B
D. consecutive
D
interior
A
0%
B. Identify
7 and
9.
A. alternate
A
interior
B. alternate
B
exterior
C. corresponding
C
0%
D
0%
C
0%
B
D. consecutive
D
interior
A
0%
C. Identify
4 and
7.
A. alternate
A
interior
B. alternate
B
exterior
C. corresponding
C
0%
D
0%
C
0%
B
D. consecutive
D
interior
A
0%
D. Identify
2 and
11.
A. alternate
A
interior
B. alternate
B
exterior
C. corresponding
C
0%
D
0%
C
0%
B
D. consecutive
D
interior
A
0%
E. Identify
3 and
5.
A. alternate
A
interior
B. alternate
B
exterior
C. corresponding
C
0%
D
0%
C
0%
B
D. consecutive
D
interior
A
0%
F. Identify
6 and
9.
A. alternate
A
interior
B. alternate
B
exterior
C. corresponding
C
0%
D
0%
C
0%
B
D. consecutive
D
interior
A
0%
Practice
12
9
10
11
2
1
4
3
7
8
6
5
Homework
pg. 144
12-19,
24-35,
41-44