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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
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
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Objective
Students will…
Use the angles formed by a
transversal to prove two lines are
parallel.
Holt McDougal Geometry
3-1 Lines and Angles
Remember!
Converse of a theorem is found by
exchanging the hypothesis and
conclusion.
***The converse of a theorem is
not automatically true.
If it is true, it must be stated as a
postulate or proved as a separate
theorem.
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Use the given information and the theorems you
have learned to show that r || s.
4

8
4  84 and 8 are alternate exterior angles.
r || s
Conv. Of Alt. Ext. s Thm.
Holt McDougal Geometry
3-1 Lines and Angles
Use the given information and the postulates
you have learned to show that l || m.
1  3
1 and 3 are
corresponding angles.
ℓ || m
Holt McDougal Geometry
Conv. of Corr. s Post.
3-1 Lines and Angles
Which postulate proves that ℓ || m?
m3 = (4x – 80)°,
m7 = (3x – 50)°, x = 30
m3 = 4(30) – 80 = 40 Substitute 30 for x.
m7 = 3(30) – 50 = 40
Substitute 30 for x.
m3 = m7
3  7
ℓ || m
Holt McDougal Geometry
Def. of  s.
Conv. of Corr. s Post.
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry