3.1 parallel lines and transversals
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3.1 Parallel Lines and Transversals
Objectives Identify the relationships between two lines
or two planes
Name angles formed by a pair of lines and a transversal
Relationships Between Lines Parallel Lines – lines that are coplanar and
do not intersect; We use the symbol || to represent parallel lines, (i.e. AB || CD).
Skew Lines – lines that do not intersect and are not coplanar
Parallel Planes – two planes that do not intersect
Name all planes that are parallel to plane AEF.
Answer: plane BHG
Example 1a:
Name all segments that intersect
Answer:
Example 1b:
Name all segments that are parallel to
Answer:
Example 1c:
Name all segments that are skew to
Answer:
Example 1d:
Use the figure to name each of the following.
Answer: plane XYZ a. Name all planes that are parallel to plane RST.
b.
c.
d.
Answer:
Answer:
Answer:
Your Turn:
Relationships Between Lines and the Angles Formed
Transversal - a line that intersects two or more coplanar lines at different points
2
4
7
1
3
5 68
Angles 1 and 5 are corresponding angles
Angles 1 and 8 are alternate exterior angles
Relationships Between Lines and the Angles Formed
Angles 3 and 6 are alternate interior angles.
Angles 3 and 5 are consecutive interior angles or same side interior angles
2
4
7
1
3
5 68
BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line v is a transversal.
Answer: w and u, w and x, w and z, u and z
Example 2a:
BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line y is a transversal.
Answer: w and u, w and x, w and z, u and z
Example 2b:
BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line u is a transversal.
Answer: v and y, y and x, v and z, y and z
Example 2c:
BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line w is a transversal.
Answer: v and y, y and x, v and z, y and z
Example 2d:
HIKING A group of nature trails is shown. Identify the sets of lines to which each given line is a transversal.
Answer: lines c, d, e, f
Answer: lines c, d, e, f
Answer: lines a, b, d, e, f
a. line a
b. line b
c. line c
d. line dAnswer: lines a, b, c, e, f
Your Turn:
Answer: corresponding
Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Example 3a:
Answer: alternate exterior
Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Example 3b:
Answer: corresponding
Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Example 3c:
Answer: alternate exterior
Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Example 3d:
Answer: alternate interior
Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Example 3e:
Answer: consecutive interior
Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Example 3f:
Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: consecutive interior
Answer: corresponding
Answer: alternate exterior
a.
b.
c.
Your Turn:
Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: alternate interior
Answer: corresponding
Answer: alternate exterior
d.
e.
f.
Your Turn:
Assignment Geometry:
Pg. 128 – 130 #4 – 48 evens
Pre-AP Geometry:Pg. 128 – 130 #4 – 48 evens, #58
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