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1.1 Points, Lines, and Planes
Identify and model points, lines and planes.Identify collinear, and coplanar points and intersecting lines and planes in the space.
VocabularyPoint, line, plane, collinear, coplanar, space, segment, ray, opposite ray, midpoint, congruent, bisects.
Prerequisite skills.
Graph and label each point in the coordinate plane.A(3, -2) B(4, 0) C(-4, - 4) D( -1, 2 )
A(3, - 2)
D(-1,2)
C(-4,- 4)
B(4,0)
Undefined terms
The terms point, line, and plane can
be explained using examples and
descriptions.
3 Undefined Terms of Geometry
• Point– Is a location.
– No dimensions.
– Represented by a small dot and by a capital letter.
AB
• line-A line is a series of points that extend in two opposite directions w/o end.-Defined by any two points on the line.-Name a line by two capital letters or a lower case letterPoints on the same line are said to be Collinear.
•
•
•
BA
Cn
ABAC BC nline
Noncollinear means not lying on the same line.
3 Undefined Terms Continues
x yz tZYXplane
plane
XYZ
• Plane– A flat surface that extends indefinitely
– Contains lines and points
– Named by 3 Noncollinear points or by a capitalscript letter.
– Points & lines in the same plane are coplanar.
– Notation: XZY or Plane
t
The last of the Undefined Terms
Through any three noncollinear points there is exactly one plane.
Geogebra
n
Segment
A segment is part of a line that consists of
two points, called endpoints, and all points
between them.
A
B
AB BA
AB ABm
Segment symbol
Length of a segment
OR
Two segments are congruent if and only if
they have equal measures, or lengths.
A D
C
3.2 cm 3.2 cm
Use “ is equal to “With numbers.
AC=DC
3.2 cm=3.2 cm
Use “ is congruent to “with figures.
DCAC
When drawing figures, show congruent
segments by making identical marking.
D
C
A
The midpoint of a segment is the point on
the segment that is the same distance
(equidistant) from both end points.
Midpoint
The midpoint bisects the segment, or
divide the segment into two congruent
segments.
D
C
2 cm
E
G2 cm
F
FDCF
FDCF
KH
L
J
KLJK
HLHJ
P
M
N
The Midpoint Formula
The Midpoint Formula :
The coordinates of the midpoint of a line segment
are the average of the coordinates of its endpoints.
2,
2
2121 yyxx
Midpoint
Number Line Coordinate Plane
Midpoint
Number Line
Midpoint
Coordinate Plane
2,
2
2121 yyxx
2
63,
2
42
)5.4 ,1(
)5.4 ,1(
Ray A Ray is part of the line that consists of one
end point an all the points of the line on
one side of the end point
A B
AB
BA
AB and are opposite rays
BA
BA
The point or set of points common to two geometric figures
k
r
A
Intersection
p
q
AB
D
C
E
If two planes intersect, then they intersect in exactly one line.
Intersection
D
FE
C
A
B
m
f
w
p
Intersection
Space
Space is a boundless, three dimensional
set of all points. Space can contain lines
and planes
E
F
C
D
G
AB
H
E
F
C
D
G
AB
H
How many planes appears in this figure?
Name three points that are collinear.
Are points G,B,C and E coplanar? Explain
At what point do and intersect? EF AB
Through any three noncollinear points there is exactly one plane.
A B
CD
E
FG
H
Which plane contains
the points: A, B, C
Which plane contains
the points: F, B, E
Which plane contains
the points: A, B, F
Use the figure to name a line containing point K.
Answer: The line can be named as line a.
There are three points on the line. Any two ofthe points can be used to name the line.
Example
Use the figure to name a plane containing point L.
Answer: The plane can be named as plane B.
You can also use the letters of any threenoncollinear points to name the plane.
plane JKM plane KLM plane JLM
Example
Draw a surface to represent plane R and label it.
Draw and label a figure for the following situation. Plane R contains lines and , which intersect at point P. Add point C on plane R so that it is not collinear with or .
Draw a line anywhere on the plane.
Draw and label a figure for the following situation. Plane R contains lines and , which intersect at point P. Add point C on plane R so that it is not collinear with or .
Draw dots on the line for points A and B. Label the points.
B
A
Draw and label a figure for the following situation. Plane R contains lines and , which intersect at point P. Add point C on plane R so that it is not collinear with or .
B
A
Draw a line intersecting .
Draw and label a figure for the following situation. Plane R contains lines and , which intersect at point P. Add point C on plane R so that it is not collinear with or .
E
D
Draw dots on this line for points D and E. Label the points.
B
A
Draw and label a figure for the following situation. Plane R contains lines and , which intersect at point P. Add point C on plane R so that it is not collinear with or .
B
A E
D P
Label the intersection point of the two lines as P.
Draw and label a figure for the following situation. Plane R contains lines and , which intersect at point P. Add point C on plane R so that it is not collinear with or .
B
A E
D PC
Draw a dot for point C in plane R such that it will not lie on or . Label the point.
Answer:
Draw and label a figure for the following situation. Plane R contains lines and , which intersect at point P. Add point C on plane R so that it is not collinear with or
Answer: 18 mm
Find the length of
Segment: The portion of the line between two points.
Find the length of .
Each inch is divided into sixteenths. Point E is closer
to the 3-inch mark.
Answer: is about 3 inches long.
Find LM.
Point M is between L and N.
Sum of parts whole
Segment Addition Postulate
LM + MN = LN
Homework
Workbook 1.1
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