objective: > understand and use the basic undefined terms and defined terms of geometry
TRANSCRIPT
1.1 Points, Lines and Planes
Objective:
> Understand and use the basic undefined terms and defined terms of
geometry.
A definition uses known words to describe a new word. In geometry, some words such as point, line and plane are undefined terms or not formally defined.
Using Undefined terms and definition
• A point has no dimension. It is usually represented by a small dot.
Using Undefined terms and definition
A
Point A
• A line extends in one dimension. It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions. In this book, lines are always straight lines.
Using Undefined terms and definition
A
B
l
Line l or AB
A plane extends in two dimensions. It is usually represented by a shape that looks like a tabletop or wall. You must imagine that the plane extends without end even though the drawing of a plane appears to have edges.
Using Undefined terms and definition
A
BC
M
Plane M or plane ABC
Must be commonly understood without being defined. One such concept is the idea that a point lies on a line or a plane.
Collinear points are points that lie on the same line.
Coplanar points are points that lie on the same plane.
A few basic concepts . . .
a. Name three points that are collinear
Solution: D, E and F lie on the
same line, so they are collinear.
Ex. 1: Naming Collinear and Coplanar Points
G
D E F
H
b. Name four points that are coplanar.
Solution: D, E, F, and G lie on the
same plane, so they are coplanar. Also D, E, F, and H are coplanar; although, the plane containing them is not drawn.
Ex. 1: Naming Collinear and Coplanar Points
G
D E F
H
The line segment or segment AB (symbolized by AB) consists of the endpoints A and B, and all points on AB that are between A and B.
More . . .
l
Line l or AB
A
A
B
B
Segment AB
The ray AB (symbolized by AB) consists of the initial point A and all points on AB that lie on the same side of A as point B.
More . . .
l
Line l or AB
A
A
B
B
Ray AB
Note that AB is the same as BA and AB is the same as BA. However, AB and BA are not the same. They have different initial points and extend in different directions.
More . . .
l
Line l or AB
A
A
B
B
Ray BA
Draw three noncollinear points J, K, and L.
Then draw JK, KL and LJ.
Ex. 2: Drawing lines, segments and rays
J
K
L
Draw J, K and L
Then draw JK
Draw three noncollinear points J, K, and L.
Then draw JK, KL and LJ.
Ex. 2: Drawing lines, segments and rays
J
K
L
Draw KL
Draw three noncollinear points J, K, and L.
Then draw JK, KL and LJ.
Ex. 2: Drawing lines, segments and rays
J
K
L
Draw LJ