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TEKS Focus:
6)(A) Verify theorems about angles formed by
the intersection of lines and line segments,
including vertical angles, and angle formed by
parallel lines cut by a transversal and prove
equidistance between the endpoints of a
segment and points on its perpendicular
bisector and apply these relationships to solve
problems.
(1)(F) Analyze mathematical relationships to
connect and communicate mathematical ideas.
(1)(A) Apply mathematics to problems arising
in everyday life, society, and the workplace.
E
A
B
Parallel
Lines
Perpendicular
Lines
Skew
Lines
Parallel
Planes
Symbol
||
T
Vocabulary Term
Name
AD || EF
AB  BC
none
AB and CG
are skew
||
Plane ABC ||
Plane EFG
F
D
C
G
Definition
Coplanar lines
that never
intersect.
Lines that
intersect at a 90⁰
or right angle.
Lines that are not
coplanar, are not
parallel, and do
not intersect.
Planes that do
not intersect.
Helpful Hint
Segments or rays are parallel,
perpendicular, or skew if the lines that
contain them are parallel, perpendicular,
or skew.
Helpful Hint
If a transversal is perpendicular to two
parallel lines, all eight angles are
congruent.
Remember
Remember that postulates are
statements that are accepted without
proof.
Identify each of the following.
A. a pair of parallel segments
LM ||QR
B. a pair of skew segments
KN and PQ
C. a pair of perpendicular segments
NS  SR
D. a pair of parallel planes
plane NMR || plane KLQ
An Ames room is a distorted room
that is used to create an optical
illusion. Two people the same
height, standing in different parts
of the room, can appear to be
different sizes.
Identify each of the following.
A. a pair of parallel segments
CD ||GH
B. a pair of skew segments
CD is skew to FG
C. a pair of perpendicular segments
DH  GH
Vocabulary Term
Transversal
Corresponding
Angles
Alternate Interior
Angles
Alternate Exterior
Angles
Same-side
Interior Angles
Definition
A line that intersects two or
more coplanar lines at two
different points.
Angles that lie on the same
side of the transversal and
in corresponding positions.
Nonadjacent interior angles
that lie on opposite sides of
the transversal.
Nonadjacent exterior
angles that lie on opposite
sides of the transversal.
Interior angles that lie on
the same side of the
transversal.
Also called consecutive
interior angles.
Example
The transversal t
intersects lines r and s
forming 8 angles.
1
3
2
4
and
and
and
and
5
7
6
8
3 and 6
4 and 5
1and 8
2 and 7
3and 5
4 and 6
Notice that the numbers on this diagram are
different from the previous diagram.
Don’t memorize the vocabulary words by #s!
Give all examples of each angle pair.
A. corresponding angles
1 & 5; 2 & 6; 3 & 7; 4 & 8
B. alternate interior angles
3 & 5 or 4 & 6
C. alternate exterior angles
1 & 7 or 2 & 8
D. same-side interior angles
3 & 6 or 4 & 5
Give one example of each angle pair.
A. corresponding angles
1 and 3
B. alternate interior angles
2 and 7
C. alternate exterior angles
1 and 8
D. same-side interior angles
2 and 3
Helpful Hint
To determine which line is the
transversal for a given angle pair,
locate the line that connects the
vertices.
Identify the transversal and classify each angle pair.
A. 1 and 3
transversal l
corr. s
B. 2 and 6
transversal n
alt. int s
Identify the transversal and classify the angle pair 2
and 5 in the diagram.
transversal n
same-side int. s.
Identify the transversal and classify
the angle pair 4 and 6 in the
diagram.
transversal m
alternate ext. s.
 EXTRA
EXAMPLES NOT USED IN
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REMEMBER TO LOG-ON TO
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LOOK AT OTHER EXAMPLES
BEFORE BEGINNING THE ON-LINE
HW AND THE WRITTEN HW.
Identify each of the following.
a. a pair of parallel segments
BF || EJ
b. a pair of skew segments
BF and DE are skew.
c. a pair of perpendicular segments
BF  FJ
d. a pair of parallel planes
plane FJH || plane BCD