8-1 Points, Lines, Planes, and Angles
Common Core State Standards
Learning Objective
7.G.5
Solve for an unknown angle using the “properties of angles.”
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8-1 Points, Lines, Planes, and Angles
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8-1 Points, Lines, Planes, and Angles
point segment right angle acute angle obtuse angle straight angle line ray complementary angles supplementary angles plane angle
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8-1 Points, Lines, Planes, and Angles
Points, lines, and planes are the building blocks of geometry. Segments, rays, and angles are defined in terms of these basic figures.
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8-1 Points, Lines, Planes, and Angles
A point names a location.
• A Point A
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8-1 Points, Lines, Planes, and Angles
A line is perfectly straight and extends forever in both directions.
B l
C line l, or BC
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8-1 Points, Lines, Planes, and Angles
A plane is a perfectly flat surface that extends forever in all directions.
D
P E
F plane P, or plane DEF
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8-1 Points, Lines, Planes, and Angles
A segment, or line segment, is the part of a line between two points.
G
H
GH
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8-1 Points, Lines, Planes, and Angles
A ray is a part of a line that starts at one point and extends forever in one direction.
K
J
KJ
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8-1 Points, Lines, Planes, and Angles
Additional Example 1: Naming Lines, Planes,
Segments, and Rays
Use the diagram to name each figure.
A. a line
Possible answers:
KL or JK
Any 2 points on a line can be used.
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8-1 Points, Lines, Planes, and Angles
Additional Example 1: Naming Lines, Planes,
Segments, and Rays
Use the diagram to name each figure.
B. a plane
Possible answers:
Plane or plane JKL
Any 3 points in the plane that form a triangle can name a plane.
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8-1 Points, Lines, Planes, and Angles
Additional Example 1: Naming Lines, Planes,
Segments, and Rays
Use the diagram to name each figure.
C. four segments
Possible answers:
JK, KL, LM, JM Write the two points in any order.
D. four rays
Possible answers: Write the endpoint first.
KJ, KL, JK, LK
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8-1 Points, Lines, Planes, and Angles
Caution!
When naming a ray always write the endpoint first.
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8-1 Points, Lines, Planes, and Angles
Check It Out!
Example 1
Use the diagram to name each figure.
A B
A. four segments
Possible answers:
AB, BC, CD, AD
B. four rays
Possible answers:
CB, CD, DA, DC
D C
Write the two points in any order.
Write the endpoint first.
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8-1 Points, Lines, Planes, and Angles
Check It Out!
Example 1
Use the diagram to name each figure.
A B
D C
C. a line
Possible answers:
AB or DC
Any 2 points on a line can be used.
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8-1 Points, Lines, Planes, and Angles
Check It Out!
Example 1
Use the diagram to name each figure.
D. a plane
Possible answers:
Plane R or plane ABC
A B
D C
Any 3 points in the plane that form a triangle can name a plane.
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8-1 Points, Lines, Planes, and Angles
Identify Ray Lines and Line Segments
Points, Lines and Planes
Lines, Line Segments & Rays Video
Planes in Three Dimensions Video
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8-1 Points, Lines, Planes, and Angles
An angle (  ) is formed by two rays, or sides, with a common endpoint called the vertex. You can name an angle several ways: by its vertex, by its vertex and a point on each ray, or by a number. When three points are used, the middle point must be the vertex.
Angles are usually measured in degrees (
(
°). Since there are 360° in a circle, one degree is of a circle.
1
360
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8-1 Points, Lines, Planes, and Angles
Holt CA Course 1

8-1 Points, Lines, Planes, and Angles
Additional Example 2: Classifying Angles
Use the diagram to name each figure.
A. a right angle
 TQS
B. two acute angles
 TQP,  RQS
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8-1 Points, Lines, Planes, and Angles
Reading Math m  TQS is read as “the measure of angle TQS.”
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8-1 Points, Lines, Planes, and Angles
Additional Example 2: Classifying Angles
Use the diagram to name each figure.
C. two obtuse angles
 SQP,  RQT
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8-1 Points, Lines, Planes, and Angles
Additional Example 2: Classifying Angles
Use the diagram to name each figure.
D. a pair of complementary angles
 TQP,  RQS m  TQP + m  RQS = 47° + 43° = 90°
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8-1 Points, Lines, Planes, and Angles
Additional Example 2: Classifying Angles
Use the diagram to name each figure.
E. two pairs of supplementary angles
 TQP,  RQT
 SQP,  SQR m  TQP + m  RQT = 47° + 133° = 180° m  SQP + m  SQR = 137° + 43° = 180°
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8-1 Points, Lines, Planes, and Angles
Check It Out!
Example 2
Use the diagram to name each figure.
A. a right angle
 BEC
A
B
C
15°
90° 75°
E
D
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8-1 Points, Lines, Planes, and Angles
Check It Out!
Example 2
Use the diagram to name each figure.
B. two acute angles
 AEB,  CED
C. two obtuse angles
 BED,  AEC
A
B
C
15°
90° 75°
E
D
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8-1 Points, Lines, Planes, and Angles
Check It Out!
Example 2
Use the diagram to name each figure.
D. a pair of complementary angles
 AEB,  CED m  AEB + m  CED = 15° + 75° = 90°
A
B
C
15°
90° 75°
E
D
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8-1 Points, Lines, Planes, and Angles
Check It Out!
Example 2

Use the diagram to name each figure.
E. two pairs of supplementary angles
AEB,  BED
 CED,  AEC m  AEB + m  BED = 15° + 165° = 180° m  CED + m  AEC = 75° + 105° = 180°
A
B
C
15°
90° 75°
E
D
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8-1 Points, Lines, Planes, and Angles
Lesson Quiz
1. Name two lines in the figure.
Possible answer: AD and BE
2. Name a right angle in the figure.
Possible answer:  AGF
3. Name a pair of complementary angles.
Possible answer:  1 and  2
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8-1 Points, Lines, Planes, and Angles
Lesson 8-1 Practice B
Lesson 8-1 Problem Solving
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