Download Holt Geometry 3-1

andand
Angles
3-1
Lines
Angles
3-1 Lines
Warm Up
Lesson Presentation
Lesson Quiz
Holt 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 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
Parallel Lines
• Def: lines that do not intersect.
• Illustration:
A
l
m
• Notation:
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B
D
C
l || m
AB || CD
3-1 Lines and Angles
Examples of Parallel Lines
•
•
•
•
Hardwood Floor
Opposite sides of windows, desks, etc.
Parking slots in parking lot
Streets: Franklin Ave & Bloomfield Ave
Holt Geometry
3-1 Lines and Angles
Perpendicular Lines
• Def: Lines that intersect to form a right angle.
m
• Illustration:
n
• Notation: m  n
• Key Fact: 4 right angles are formed.
Holt Geometry
3-1 Lines and Angles
Example of Perpendicular Lines
• Streets: Franklin Ave and Center Street
Holt Geometry
3-1 Lines and Angles
Skew Lines
• Def: (NOT coplanar) Skew lines are NOT
parallel lines and do not intersect
• Illustration:
• Notation: AE and CD are skew.
Holt Geometry
3-1 Lines and Angles
Holt Geometry
3-1 Lines and Angles
Skew lines continued
• Are the following lines skew…?
1. AE and FB? No, they are ||
2. FB and CG?
No, they are || --
even though we
can’t see it, a plane COULD connect them
Yes, they are skew
3. AE and BD?
Holt Geometry
3-1 Lines and Angles
Parallel Planes
are planes that do not intersect.
Plane AEB || plane CGH
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
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
Example 1: Identifying Types of Lines and Planes
Identify each of the following.
E. a pair of parallel segments
LM ||QR
F. a pair of skew segments
KN and PQ
G. a pair of perpendicular segments
NS  SP
H. a pair of parallel planes
plane NMR || plane KLQ
Holt Geometry
3-1 Lines and Angles
Lesson Quiz: Part I
Identify each of the following.
I. a pair of parallel segments
EH || FG
J. a pair of skew segments
BF and EH
K. a pair of perpendicular segments
CG  GH
L. a pair of parallel planes
ABC and EFG
Holt Geometry
3-1 Lines and Angles
Parallel
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neither
perpedicular
3-1 Lines and Angles
No, they intersect
Yes, they are skew.
Holt Geometry
3-1 Lines and Angles
Plane C
Plane D
Holt Geometry
3-1 Lines and Angles
1. Line x and line y
2. Line x and line z
3. Line y and line z
Holt Geometry
3-1 Lines and Angles
4.
QU TX
ST
RQ
5. Plane RST
6. WS WX UV RV
Holt Geometry