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andand
Angles
3-1
Lines
Angles
3-1Lines
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Geometry
HoltMcDougal
McDougalGeometry
Geometry
3-1 Lines and Angles
Warm Up
Identify each of the following.
1.
points that lie in the same plane
coplanar points
2. two angles whose sum is 180°
supplementary angles
3. the intersection of two distinct intersecting lines
point
4. a pair of adjacent angles whose non-common
sides are opposite rays
linear pair
Holt McDougal Geometry
3-1 Lines and Angles
Objectives
Identify parallel, perpendicular, and
skew lines.
Identify the angles formed by two lines
and a transversal.
Holt McDougal Geometry
3-1 Lines and Angles
Vocabulary
parallel lines
perpendicular lines
skew lines
parallel planes
transversal
corresponding angles
alternate interior angles
alternate exterior angles
same-side interior angles
Holt McDougal Geometry
Parallel Lines and Planes
You will learn to describe relationships among lines,
parts of lines, and planes.
In geometry, two lines in a plane that are always the same
parallel lines
distance apart are ____________.
No two parallel lines intersect, no matter how far you extend them.
3-1 Lines and Angles
Holt McDougal Geometry
Parallel Lines and Planes
Planes can also be parallel.
The shelves of a bookcase are examples of parts of planes.
The shelves are the same distance apart at all points, and do not appear to
intersect.
parallel
They are _______.
parallel planes
In geometry, planes that do not intersect are called _____________.
Q
R
Plane PSR || plane JML
Plane JPQ || plane MLR
Plane PJM || plane QRL
P
J
K
S
L
M
3-1 Lines and Angles
Helpful Hint
Segments or rays are parallel,
perpendicular, or skew if the lines
that contain them are parallel,
perpendicular, or skew.
Holt McDougal Geometry
3-1 Lines and Angles
Example 1: Identifying Types of Lines and Planes
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  SP
D. a pair of parallel planes
plane NMR || plane KLQ
Holt McDougal Geometry
3-1 Lines and Angles
Check It Out! Example 1
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
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Example 2: Classifying Pairs of Angles
Give an example of each angle pair.
A. corresponding angles
 1 and  5
B. alternate interior angles
 3 and  5
C. alternate exterior angles
 1 and  7
D. same-side interior angles
 3 and  6
Holt McDougal Geometry
3-1 Lines and Angles
Check It Out! Example 2
Give an 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
Holt McDougal Geometry
3-1 Lines and Angles
Helpful Hint
To determine which line is the
transversal for a given angle pair,
locate the line that connects the
vertices.
Holt McDougal Geometry
3-1 Lines and Angles
Example 3: Identifying Angle Pairs and Transversals
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
C.  4 and  6
transversal m
alt. ext  s
Holt McDougal Geometry
3-1 Lines and Angles
Check It Out! Example 3
Identify the transversal and classify the angle
pair  2 and  5 in the diagram.
transversal n
same-side int.  s.
Holt McDougal Geometry
3-1 Lines and Angles
Lesson Quiz: Part I
Identify each of the following.
1. a pair of parallel segments
EH || FG
2. a pair of skew segments
BF and EH
3. a pair of perpendicular segments
CG  GH
4. a pair of parallel planes
ABC and EFG
Holt McDougal Geometry
3-1 Lines and Angles
Lesson Quiz: Part II
Identify each of the following.
5. one pair alternate interior
angles
 EHG and  HGK
6. One pair corresponding angles
 EHG and  FGJ
7. one pair alternate exterior angles
 IHE and  JGK
8. one pair same-side interior angles
 EHG and  HGF
Holt McDougal Geometry
Transversals and Corresponding Angles
Types of angle pairs formed when
a transversal cuts two parallel lines.
Concept
Summary
Congruent
alternate interior
Supplementary
consecutive interior
alternate exterior
corresponding
?
5