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andand
Angles
3-1
Lines
Angles
3-1 Lines
Bellwork
1. Find the better buy.
8 apples for $6.80
9 apples for $7.70
10 apples for $8.50
12 apples for $9.60
2. If f(x) = 2x/3 and g(x) = x – 2 and f(x) = g(x),
Find the value of x.
a. 0
b. 2
3. 3x – 2y = 1 ; y
Holt Geometry
c. 4
d. 6
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 Geometry
3-1 Lines and Angles
Objectives
Identify parallel, perpendicular, and
skew lines.
Identify the angles formed by two lines
and a transversal.
Holt 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 Geometry
3-1 Lines and Angles
Holt Geometry
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 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 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 Geometry
3-1 Lines and Angles
Holt 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 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 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 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 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 Geometry
3-1 Lines and Angles
Practice Time!
p. 148 #14=32, 44-48,
55,59,61
Holt 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 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 Geometry