parallel lines and transversals
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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 alternate exterior angles alternate interior angles corresponding angles. - PowerPoint PPT PresentationTRANSCRIPT
Parallel Lines Parallel Lines and and
TransversalsTransversalsChapter 3-1Chapter 3-1
Lesson 3-1 Ideas/Vocabulary
• Identify the relationships between two lines or two planes.
• parallel lines
• Name angles formed by a pair of lines and a transversal.
• parallel planes• skew lines• transversal
• consecutive interior angles• alternate exterior angles• alternate interior angles• 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. // to AB and containing D2. to AB and containing D3. Skew to AB and containing D4. Name the plane(s) that contain D and appear to
be // to plane ABE
A D
E H
B C
GF
1. DC1. DC
2. AD2. AD
3. DH3. DH 4. DCH or DGH or DCG4. DCH or DGH or DCG
Lesson 3-1 Example 1a
A. Name all planes that are parallel to plane AEF.
Identify Relationships
Answer: plane BHG
Lesson 3-1 Example 1b
__B. Name all segments that intersect AF.
Identify Relationships
Answer: EF, GF, DA, and BA__ __ __ __
Lesson 3-1 Example 1c
__C. Name all segments that are skew to AD.
Identify Relationships
Answer: FG, GB, EH, EC, and CH__ __ __ __ __
Lesson 3-1 CYP 1a
A B
C D
0% 0%0%0%
A. A
B. B
C. C
D. D
A.Name a plane that is parallel to plane RST.
plane WTZ
plane SYZ
plane WXY
plane QRX
Lesson 3-1 CYP 1b
A B
C D
0% 0%0%0%
B. Name a segment that intersects YZ.
XY
WX
QW
RSA.
B.
C.
D.
0% 0%0%0%
Lesson 3-1 CYP 1c
C. Name a segment that is parallel to RX.
A.
B.
C.
D.
ZW
TZ
QR
ST
A. A
B. B
C. C
D. D
RX
ST
XW
QW
__
__
___
___
Lesson 3-1 CYP 1d
A B
C D
0% 0%0%0%
D. Name a segment that is skew to TZ.
__
Transversal• A line that intersects two or more coplanar
lines at different points.
t
1 23 4
5 6
7 8
t is a transversal
Lesson 3-1 Example 2a
Identify TransversalsA. 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.
Lesson 3-1 Example 2b
Identify TransversalsB. 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
Lesson 3-1 Example 2c
Identify TransversalsC. 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
Lesson 3-1 CYP 2a
A B
C D
0% 0%0%0%
A. A
B. B
C. C
D. D
A. HIKING A group of nature trails is shown. Identify the sets of lines to which line a is a transversal.
lines c, f
lines c, d, e
lines c, d, f
lines c, d, e, f
Lesson 3-1 CYP 2b
A B
C D
0% 0%0%0%
A. A
B. B
C. C
D. D
B. HIKING A group of nature trails is shown. Identify the sets of lines to which line b is a transversal.
no lines
lines c, f
lines c, d, e, f
lines a, c, d, e, f
Lesson 3-1 CYP 2c
A B
C D
0% 0%0%0%
A. A
B. B
C. C
D. D
C. HIKING A group of nature trails is shown. Identify the sets of lines to which line c is a transversal.
lines a, b
lines a, b, d, e, f
lines a, d, f
lines a, b, e
Lesson 3-1 CYP 2d
A B
C D
0% 0%0%0%
A. A
B. B
C. C
D. D
D. HIKING A group of nature trails is shown. Identify the sets of lines to which line d is a transversal.
lines e, f
lines a, b, f
lines a, b, c, e, f
lines a, b, c
Corresponding Angles• Two angles that occupy corresponding
positions.
t
1 23 4
5 6
7 8
1 and 5 are corresponding s2 and 6 are corresponding s3 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 23 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 23 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 23 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
Lesson 3-1 Example 3a
Identify Angle Relationships
Answer:
corresponding
A. Identify 7 and 3 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Lesson 3-1 Example 3b
Identify Angle Relationships
B. Identify 8 and 2 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer:
alternate exterior
Lesson 3-1 Example 3c
Identify Angle Relationships
C. Identify 4 and 11 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer:
corresponding
Lesson 3-1 Example 3d
Identify Angle Relationships
D. Identify 7 and 1 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer:
alternate exterior
Lesson 3-1 Example 3e
Identify Angle Relationships
E. Identify 3 and 9 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer:
alternate interior
Lesson 3-1 Example 3f
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.
Lesson 3-1 CYP 3a
A B
C D
0% 0%0%0%
A. A
B. B
C. C
D. D
alternate interior
alternate exterior
corresponding
consecutive interior
B. Identify 7 and 9.
Lesson 3-1 CYP 3b
A B
C D
0% 0%0%0%
A. A
B. B
C. C
D. D
alternate interior
alternate exterior
corresponding
consecutive interior
C. Identify 4 and 7.
Lesson 3-1 CYP 3c
A B
C D
0% 0%0%0%
A. A
B. B
C. C
D. D
alternate interior
alternate exterior
corresponding
consecutive interior
D. Identify 2 and 11.
Lesson 3-1 CYP 3d
A B
C D
0% 0%0%0%
A. A
B. B
C. C
D. D
alternate interior
alternate exterior
corresponding
consecutive interior
E. Identify 3 and 5.
Lesson 3-1 CYP 3e
A B
C D
0% 0%0%0%
A. A
B. B
C. C
D. D
alternate interior
alternate exterior
corresponding
consecutive interior
F. Identify 6 and 9.
Lesson 3-1 CYP 3e
A B
C D
0% 0%0%0%
A. A
B. B
C. C
D. D
alternate interior
alternate exterior
corresponding
consecutive interior
Practice
1 432
8 567
11
91012
Homework pg. 14412-19, 24-35, 41-44