Download 1.1: The Building Blocks of Geometry

1.1: The Building
Blocks of Geometry
Expectation:
G1.1.6:
Recognize Euclidean geometry as an axiom
system. Know the key axioms and
understand the meaning of and distinguish
between undefined terms (e.g., point, line,
and plane), axioms, definitions, and
theorems.
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1.1: The Building Blocks of Geometry
Undefined Terms
1.
2.
3.
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1.1: The Building Blocks of Geometry
Points
0 dimensional (have no size)
Models of points
-Dots
-Stars in the sky
-Cities on a map
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1.1: The Building Blocks of Geometry
Points
Naming points
- Use capital letters
A
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1.1: The Building Blocks of Geometry
Lines
Perfectly straight extending
infinitely without thickness.
1 dimensional
Models of Lines
- roads
- hallway
- edge of a box
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1.1: The Building Blocks of Geometry
Naming Lines
l
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Line
l
1.1: The Building Blocks of Geometry
Naming Lines
B
A
Line AB or BA
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1.1: The Building Blocks of Geometry
Planes
Infinite, flat surface without
thickness.
2 dimensional
Models of Planes
-desktop
-wall
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-rooftop
1.1: The Building Blocks of Geometry
Drawing Planes
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1.1: The Building Blocks of Geometry
Naming Planes
R
Plane R
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1.1: The Building Blocks of Geometry
Naming Planes
Q
P
R
Plane PQR, PRQ, RPQ,
RQP, QRP or QPR
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1.1: The Building Blocks of Geometry
Collinear Points
Defn:Three or more points are
collinear iff they are on the
same line.
A
B
C
A, B and C are collinear.
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1.1: The Building Blocks of Geometry
Coplanar Points
Defn: Four or more points are
coplanar iff they are on the same
plane.
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1.1: The Building Blocks of Geometry
Coplanar Points
Q
S
P
R
P, Q, R and S are coplanar points.
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1.1: The Building Blocks of Geometry
Segments
Defn: A segment is a part of a
line that begins at one point and
ends at another. The points are
called the endpoints of the
segment.
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1.1: The Building Blocks of Geometry
Segments
A
B
AB
This is not a segment!!!
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1.1: The Building Blocks of Geometry
Segments
A
B
The segment with endpoints A
and B: denoted AB or BA
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1.1: The Building Blocks of Geometry
Rays
Defn: A ray is a part of a line that
starts at a point and extends
infinitely in one direction. The
point is called the endpoint of the
ray.
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1.1: The Building Blocks of Geometry
Rays
Z
Y
The ray with endpoint Y
containing Z: denoted YZ (may
not be denoted
ZY or ZY).
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1.1: The Building Blocks of Geometry
Angles
Defn: An angle is a figure formed
by two rays with a common
endpoint. The common endpoint is
called the vertex of the angle and
the two rays are called the sides of
the angle.
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1.1: The Building Blocks of Geometry
Angles
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1.1: The Building Blocks of Geometry
Angles
sides of
the angle
vertex of
the angle
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1.1: The Building Blocks of Geometry
Naming an Angle
There are 3 ways to name an
angle: ( represents an angle)
1. The vertex.
2. A point from each side and
the vertex (vertex is
between the other points).
3. A number.
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1.1: The Building Blocks of Geometry
Naming Angles
A
C
1
B
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1.1: The Building Blocks of Geometry
Naming Angles
A
C
1
B
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B
1.1: The Building Blocks of Geometry
Naming Angles
A
C
1
B
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ABC or CBA
1.1: The Building Blocks of Geometry
Naming Angles
A
C
1
B
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1
1.1: The Building Blocks of Geometry
Intersect and
Intersections
If 2 figures share one or more
points, then they intersect. The
point or points they have in
common is called their
intersection.
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1.1: The Building Blocks of Geometry
Postulates
A postulate is a statement that is
accepted as being true without
proof.
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1.1: The Building Blocks of Geometry
Complete Activity 1.1 on page
12.
You may work in pairs.
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1.1: The Building Blocks of Geometry
Intersecting Lines
Postulate
If two lines intersect, then their
intersection is a point.
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1.1: The Building Blocks of Geometry
Intersecting Planes
Postulate
If two planes intersect, then their
intersection is a line.
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1.1: The Building Blocks of Geometry
Unique Line Postulate
Through any two distinct points,
there is a unique (one and only
one) line.
Sometimes this is stated in an
alternate form: ”Two points
determine exactly one line.”
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1.1: The Building Blocks of Geometry
Unique Plane Postulate
Through any 3 noncollinear points
there is a unique plane.
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1.1: The Building Blocks of Geometry
Flat Plane Postulate
If two points are in a plane, then the
line containing them is in the
plane.
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1.1: The Building Blocks of Geometry
Dimension Postulate
Given a line in a plane, there is at least
one point in the plane that is not on the
line.
Given a plane in space, there is at least
one point in space not on the plane.
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1.1: The Building Blocks of Geometry
Assignment:
pages 14 – 15, # 9 – 48
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1.1: The Building Blocks of Geometry