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Geometry Bellwork 9/16/14
Section 3.1
Identify Pairs of Lines and Angles
Key Concepts:
Diagram
Parallel lines:
Lines that do not intersect and
are coplanar. Lines m and n.
Skew lines:
Lines that do not intersect and
are NOT coplanar. Lines m and k.
Parallel planes:
Planes that do not intersect.
Planes T and U.
EXAMPLE 1
Identify relationships in space
Think of each segment in the figure as part of a line.
Complete the statements.
a. Name the 3 lines parallel to CD .
AB , HG, EF
b. Name the 4 lines perpendicular to AH .
HG , EH , AB, DA
c. Name the 5 lines skew to ED.
HG, FG, AB, CB, AG
d. Is plane EFG parallel, skew, or perpendicular to plane
CFG?
perpendicular
Section 3.1
Identify Pairs of Lines and Angles
PARALLEL AND PERPENDICULAR LINES
Two lines
that are in the same plane are either __________(
parallel
perpendicular
___________________
(
parallel
do not intersect
),
oblique
), or ___________.
perpendicular
intersect at 90°
oblique
intersect NOT at 90°
Section 3.1
Identify Pairs of Lines and Angles
Postulates:
Postulate 13: Parallel Postulate
If there is a line and a point not on the
line, then there is exactly one line
through the point parallel to the given
line.
There is exactly one line through
P parallel to l.
Postulate 14: Perpendicular Postulate
If there is a line and a point not on the
line, then there is exactly one line
through the point perpendicular to the
given line.
There is exactly one line through
P perpendicular to l.
EXAMPLE 2
Identify parallel and perpendicular lines
Use the markings in the diagram.
a. Name a pair of parallel lines.
MK LS
b. Name a pair of perpendicular lines.
NP
c. Is PR
PQ
LS ? Explain.
No, no parallel markings
on PR .
GUIDED PRACTICE
for Examples 1 and 2
1. Lines in the same plane that do not intersect are
parallel
called________________.
2. Lines not in the same plane that do not intersect
skew
are called________________.
Section 3.1
Identify Pairs of Lines and Angles
ANGLES AND TRANVERSALS
transversal is a
A _____________
line that intersects two or more coplanar lines at
_______
points
different __________.
Transversals form special angle
pairs
_________.
Name the transversals in each diagram.
line t
line b
line a
Section 3.1
Identify Pairs of Lines and Angles
Key Concepts: Angles formed by transversals
Corresponding angles:
Two angles that have corresponding positions on the same
side of a transversal.
Section 3.1
Identify Pairs of Lines and Angles
Key Concepts: Angles formed by transversals
Consecutive interior angles:
Two angles that lie between the two lines on the same
side of a transversal.
Section 3.1
Identify Pairs of Lines and Angles
Key Concepts: Angles formed by transversals
Alternate interior angles:
Two angles that lie between the two lines on opposite
sides of a transversal.
Section 3.1
Identify Pairs of Lines and Angles
Key Concepts: Angles formed by transversals
Alternate exterior angles:
Two angles that lie outside the two lines on opposite
sides of a transversal.
EXAMPLE 3
Identify angle relationships
Identify all pairs of angles of the given type.
Transversal connects angle pairs
a. Corresponding
Same side transversal, corresponding spots
1, 5
3, 7
2, 6
4, 8
b. Alternate interior
Alternate sides, between two lines
2, 7
4, 5
c. Alternate exterior
Alternate sides, outside two lines
1, 8
3, 6
d. Consecutive interior
Same side, between two lines
2, 5
4, 7
GUIDED PRACTICE
for Example 3
Classify the pair of numbered angles.
3.
Corresponding (CORR)
GUIDED PRACTICE
for Example 3
Classify the pair of numbered angles.
4.
Alternate Exterior (AE)
GUIDED PRACTICE
for Example 3
Classify the pair of numbered angles.
5.
Alternate Interior (AI)
HOMEWORK
Worksheet 3.1
Worksheet 3.1
Skip #’s 25 to 30