3-1: Lines and Angles

1. Holt Geometry
3-1 Lines and Angles3-1 Lines and Angles
Holt Geometry
Warm UpWarm Up
Lesson PresentationLesson Presentation
Lesson QuizLesson Quiz

2. Holt Geometry
3-1 Lines and Angles
Warm Up
Identify each of the following.
1. points that lie in the same plane
2. two angles whose sum is 180°
3. the intersection of two distinct intersecting lines
4. a pair of adjacent angles whose non-common
sides are opposite rays
coplanar points
supplementary angles
point
linear pair

3. Holt Geometry
3-1 Lines and Angles
Identify parallel, perpendicular, and
skew lines.
Identify the angles formed by two lines
and a transversal.
Objectives

4. Holt Geometry
3-1 Lines and Angles
parallel lines
perpendicular lines
skew lines
parallel planes
transversal
corresponding angles
alternate interior angles
alternate exterior angles
same-side interior angles
Vocabulary

5. Holt Geometry
3-1 Lines and Angles

6. Holt Geometry
3-1 Lines and Angles
Segments or rays are parallel,
perpendicular, or skew if the lines
that contain them are parallel,
perpendicular, or skew.
Helpful Hint

7. 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
B. a pair of skew segments
C. a pair of perpendicular segments
D. a pair of parallel planes
LM ||QR
KN and PQ
NS ⊥ SP
plane NMR || plane KLQ

8. Holt Geometry
3-1 Lines and Angles
Check It Out! Example 1
Identify each of the following.
a. a pair of parallel segments
b. a pair of skew segments
d. a pair of parallel planes
c. a pair of perpendicular segments
BF || EJ
BF and DE are skew.
BF ⊥ FJ
plane FJH || plane BCD

9. Holt Geometry
3-1 Lines and Angles

10. Holt Geometry
3-1 Lines and Angles
Example 2: Classifying Pairs of Angles
Give an example of each angle pair.
A. corresponding angles
B. alternate interior angles
C. alternate exterior angles
∠1 and ∠5
D. same-side interior angles
∠3 and ∠5
∠1 and ∠7
∠3 and ∠6

11. Holt Geometry
3-1 Lines and Angles
Check It Out! Example 2
Give an example of each angle pair.
A. corresponding angles
B. alternate interior angles
C. alternate exterior angles
∠1 and ∠3
D. same-side interior angles
∠2 and ∠7
∠1 and ∠8
∠2 and ∠3

12. Holt Geometry
3-1 Lines and Angles
To determine which line is the
transversal for a given angle pair,
locate the line that connects the
vertices.
Helpful Hint

13. 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
B. ∠2 and ∠6
C. ∠4 and ∠6
transversal l
corr. ∠s
transversal n
alt. int ∠s
transversal m
alt. ext ∠s

14. 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.

15. Holt Geometry
3-1 Lines and Angles
Lesson Quiz: Part I
Identify each of the following.
1. a pair of parallel segments
2. a pair of skew segments
3. a pair of perpendicular segments
4. a pair of parallel planes
EH || FG
BF and EH
CG ⊥ GH
ABC and EFG

16. Holt Geometry
3-1 Lines and Angles
Lesson Quiz: Part II
Identify each of the following.
5. one pair alternate interior
angles
6. One pair corresponding angles
7. one pair alternate exterior angles
∠EHG and ∠HGK
8. one pair same-side interior angles
∠EHG and ∠FGJ
∠IHE and ∠JGK
∠EHG and ∠HGF