Parallel Lines and Planes

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Parthenon Athens
Dallas City Hall I.M. Pei
Havasu Falls I.M. Pei
Parallel Lines and Planes
3.1 Written Exercises
2
3.1 Written Exercises
1
Classify each pair of angles as either alternate
interior, same-side interior, or corresponding.
Alternate exterior angles Z points the way.
3
2
Classify each pair of angles as either alternate
interior, same-side interior, or corresponding.
Corresponding angles Same position on ladder
4
3
Classify each pair of angles as either alternate
interior, same-side interior, or corresponding.
Same-side interior angles C points the way.
5
4
Classify each pair of angles as either alternate
interior, same-side interior, or corresponding.
Alternate interior angles Z points the way.
6
5
Classify each pair of angles as either alternate
interior, same-side interior, or corresponding.
Corresponding angles Same position on ladder
7
6
Classify each pair of angles as either alternate
interior, same-side interior, or corresponding.
Corresponding angles Same position on ladder
8
7
Name the two lines and transversal that form each
pair of angles.
9
8
Name the two lines and transversal that form each
pair of angles.
10
9
Name the two lines and transversal that form each
pair of angles.
Not appropriate Because the lines Are not
parallel.
11
10
Name the two lines and transversal that form each
pair of angles.
12
11
Name the two lines and transversal that form each
pair of angles.
13
Classify each pair of angles as either alternate
interior, same-side interior, or corresponding.
12
Corresponding angles Same position on ladder
14
Classify each pair of angles as either alternate
interior, same-side interior, or corresponding.
13
Corresponding angles Same position on ladder
15
Classify each pair of angles as either alternate
interior, same-side interior, or corresponding.
14
Alternate interior angles Z points the way.
16
Classify each pair of angles as either alternate
interior, same-side interior, or corresponding.
15
Same-side interior angles C points the way.
17
Classify each pair of angles as either alternate
interior, same-side interior, or corresponding.
16
Same-side interior angles C points the way.
18
Classify each pair of angles as either alternate
interior, same-side interior, or corresponding.
17
Corresponding angles Same position on ladder
19
Alternate exterior angles
Alternate interior angles Z points the way.
Corresponding angles Same position on ladder
Same-side interior angles C points the way.
Same-side exterior angles
20
23
Name 5 lines that appear to be // to
21
24
Name 3 lines that appear to be // to
22
25
Name 4 lines that appear to be skew to
23
26
Name 2 planes that appear to be // to
24
26
Name 2 planes that appear to be // to
25
27
Name 4 planes that appear to be // to
26
27
Name 4 planes that appear to be // to
27
27
Name 4 planes that appear to be // to
28
28
How many pairs of parallel planes are shown?
29
28
How many pairs of parallel planes are shown?
30
28
How many pairs of parallel planes are shown?
31
28
How many pairs of parallel planes are shown?
32
29
Suppose the top and bottom of the box lie in
parallel planes. Explain how Theorem 3.1 can be
used to prove
33
29
Suppose the top and bottom of the box lie in
parallel planes. Explain how Theorem 3.1 can be
used to prove
Theorem 3.1 If 2 parallel planes are cut by a
third plane, then the lines of intersection are
parallel.
34
29
Suppose the top and bottom of the box lie in
parallel planes. Explain how Theorem 3.1 can be
used to prove
Theorem 3.1 If 2 parallel planes are cut by a
third plane, then the lines of intersection are
parallel.
Are the lines of intersection of the transversal
plane CDJI.
35
Complete each statement with always, sometimes,
or never.
30
When there is a transversal of two lines, the 3
lines are __________ coplanar.
always
Since two points of each line are in the same
plane, all the lines are in the same
plane. Remember, if 2 points of a line are in
the plane, then the whole line is in the plane.
36
Complete each statement with always, sometimes,
or never.
Three lines intersecting in one point
are ___________ coplanar.
31
Yes
37
Complete each statement with always, sometimes,
or never.
Three lines intersecting in one point
are ___________ coplanar.
31
sometimes
No
Yes
38
Complete each statement with always, sometimes,
or never.
32
never
Two lines that are not coplanar ________
intersect.
Intersecting lines are always coplanar And Non-int
ersecting are never coplanar.
39
Complete each statement with always, sometimes,
or never.
33
always
Two lines parallel to a third line are ________
parallel to each other
40
Complete each statement with always, sometimes,
or never.
sometimes
34
Two lines skew to a third line are __________
skew to each other.
No
No
Yes
41
Complete each statement with always, sometimes,
or never.
35
Two lines perpendicular to a third line are
__________ perpendicular to each other.
sometimes
No
Yes
No
42
Complete each statement with always, sometimes,
or never.
36
Two planes parallel to the same line are
__________ parallel to each other.
sometimes
Yes
No
43
Complete each statement with always, sometimes,
or never.
37
Two planes parallel to the same plane are
__________ parallel to each other.
always
44
Complete each statement with always, sometimes,
or never.
38
sometimes
Lines in two parallel planes are _________
parallel to each other.
Yes
No
45
Complete each statement with always, sometimes,
or never.
39
Two lines parallel to the same plane are
_________ parallel to each other.
sometimes
Yes
No
46
Cest fini.
Good day and good luck.