Transcript Ch 8-1 Points, Lines, Planes, and Angles

8-1 Points, Lines, Planes, and Angles
California
Standards
Preparation for MG3.1 Identify and
construct basic elements of geometric figures
(e.g., altitudes, midpoints, diagonals, angle
bisectors, and perpendicular bisectors;
central angles, radii, diameters, and chords of
circles) by using a compass and straightedge.
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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.
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•A
Point A
8-1 Points, Lines, Planes, and Angles
A line is perfectly
straight and
extends forever in
both directions.
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l
B
C
line l, or BC
8-1 Points, Lines, Planes, and Angles
A plane is a
perfectly flat
surface that
extends forever in
all directions.
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P
D
E
F
plane P, or
plane DEF
8-1 Points, Lines, Planes, and Angles
A segment, or
line segment, is
the part of a line
between two
points.
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H
G
GH
8-1 Points, Lines, Planes, and Angles
A ray is a part of
a line that starts
at one point and
extends forever in K
one direction.
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J
KJ
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
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Any 2 points on a line
can be used.
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
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or plane JKL
Any 3 points in the plane
that form a triangle can
name a plane.
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
D. four rays
Possible answers:
KJ, KL, JK, LK
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Write the two points in
any order.
Write the endpoint first.
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
A. four segments
D
B
C
Possible answers:
AB, BC, CD, AD
B. four rays
Write the two points in
any order.
Possible answers:
CB, CD, DA, DC
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Write the endpoint first.
8-1 Points, Lines, Planes, and Angles
Check It Out! Example 1
Use the diagram to name each figure.
A
C. a line
D
B
C
Possible answers:
AB or DC
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Any 2 points on a line
can be used.
8-1 Points, Lines, Planes, and Angles
Check It Out! Example 1
Use the diagram to name each figure.
D. a plane
A
D
Possible answers:
Plane R or plane ABC
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B
C
Any 3 points in the plane
that form a triangle can
name a plane.
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
(
1
there are 360° in a circle, one degree is
of a
360
circle.
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8-1 Points, Lines, Planes, and Angles
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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 mTQP + m RQT = 47° + 133° = 180°
SQP, SQR 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
C
B
A
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15°
90°
E
75°
D
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
C
B
A
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15°
90°
E
75°
D
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°
C
B
A
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15°
90°
E
75°
D
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 mAEB + mBED = 15° + 165° = 180°
CED, AEC mCED + mAEC = 75° + 105° = 180°
C
B
A
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15°
90°
E
75°
D