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Unit 4 Day 1 NotesPoints, Lines and Planes
Definitions:Point: A location in space having no dimension.
Line: A set of points extending indefinitely in two opposite directions having only one dimension, length.
Plane: A set of points extending indefinitely in all directions along a flat surface having two dimensions, length and width.
Collinear Points: Points that lie on an unique line.
Coplanar Points: Points that lie on an unique plane.
Coplanar Lines: Lines that lie on a unique plane.
Points, Lines and Planes
Definitions:Intersection:
A) of 2 Lines: The single point where two or more lines cross.
B) of a Line and a Plane:The single point where a line crosses through a plane.
C) of 2 Planes: The single line where two or more planes cross.
Parallel Lines: Coplanar lines that do not intersect.
Skew Lines: Non-coplanar lines that do not intersect.
Labeling:
Points are labeled with a capital letter.
Points, Lines and Planes
Labeling:
Lines are labeled by identifying two points on that line (Collinear Points)
orBuy a single lower case script letter.
Points, Lines and Planes
Labeling:
Planes are labeled by identifying three points on that plane (Coplanar Points)
orBuy a single upper case script letter.
Plane LMN or Plane R
Points, Lines and Planes
Labeling:
List statements that describe what you see in the picture above
1.)2.)3.)4.)5.)6.)7.)8.)
Points, Lines and Planes
CW(1):
Write ten statements that describe things that you see in the picture above.
Points, Lines and Planes
Definitions:Congruent: Two or more geometric shapes
that are identical in size and shape.
Line Segment: A part of a line that begins on one point and ends on a second point.
End Point: The point on which a line segment either begins or ends. (Also, the point on which a ray starts.) (A line has two end point and a ray only has one end point)
Ray: A part of a line that begins on a point and goes on to infinity in one direction.
Segment Length: The measure of a line segment.
Congruent Segments: Two or more line segments that are equal in length.
Points, Lines and Planes
Definitions:Midpoint: The point on a line segment that is
the same distance from both end points of that segment.
Segment Bisector: A line, ray or segment that intersects a line segment at the midpoint.
Segment Addition Postulate: If point B lies on line segment AC then the length of line segment AB plus the length of line segment BC equals the length of line segment AC.
A B C
AB + BC = AC
Points, Lines and Planes
A
B
C
D
You can write two segments are congruent with the shorthand below.
If two segments are congruent, you also know that their lengths are equal.
NOTICE: The shorthand for writing a segment is just a bar over the two letters. If there was an arrow on each end
of the bar that would be shorthand for a line.
NOTICE: When you are referring to a length of line segment you use just the two endpoints with NO special
notation over the letters.
Points, Lines and Planes
M
N S
R
You can say NOTHING about how the rays are related!
Rays can NEVER be congruent!
You can only name the two rays. When naming a ray you ALWAYS start with the end point followed
by a point on the ray.
NOTICE: The shorthand notation for rays only has a one directional arrow over the top of it. The end of the
directional WITHOUT the arrow is always of the endpoint of the ray.
Points, Lines and Planes
Review:Segment Addition Postulate:
If point B lies on line segment AC then the length of line segment AB plus the length of line segment BC equals the length of line segment AC.
A B C
AB + BC = AC
If AB = 4 and BC = 7,what is the length of AC?
F G H
If FG = 10 and GH = 13,what is the length of segment FH?
Points, Lines and Planes
Review:
A B C
Segment Addition works exactly the same whether you have numbers or variables.
AB = 3x – 4BC = 2x + 15
What is the length of segment AC?
F G H
You can also use Segment Addition to find the lengths of the smaller segments.
FH = 9x + 2FG = 4x + 6
What is the length of segment GH?
REMEMBERFG + GH = FH
SoGH = FH - FG
Points, Lines and Planes
CW(2):In the figure below, B is the midpoint of . Find value of x and length of AC.
AC
A B C
2x + 12 5x + 10
Find value of x and length of RS and ST.
R S T
2x - 4 3x + 7
RT = 43
In the figure below, C is the midpoint of . Find value of x and length of AC.
AB
A C B
5x - 6 2x
Points, Lines and Planes
CW(2) Cont.:If RT = 60, find x, RS and ST.
R S T
3x - 12 2x - 8
If G is the mid point of , find x and EG.EF
F
G
E
3x
36 - x
Points, Lines and Planes
Use the figure below to decide whether each statement is true or false. Explain why each statement is true or false on your own paper!
T S V
B
Q
P
W R
1) bisect 5) is longer than
2)S is the midpoint of 6) V is the midpoint of TW
3) 7) WR QV
4) bisects 8)
PB RS SW VR
TV
SV TS
W VR
# #
TB + BW = TW
Given that point A lies between points C and T, find each missing value. (Hint: Draw and label a diagram for each problem.)
9) CA = 6 11) CA = ?AT = ? AT = 5.5CT = 15 CT = 10.75
10) CA = 5.2 12) CA = 22AT = 4.8 AT = ?CT = ? CT = 35
HW:Points, Lines and Planes
HW:For each figure, find x and the indicated segment measure. Show all work on your own paper!
13) B is the midpoint of . AC
A B
C
AB = 4x – 3BC = xAC = ?
14) E is the midpoint of . DF
D EF
DF = x + 6DE = x - 1EF = ?
15) bisects BX TW X
B
T WWB = x + 5TW = 4x + 5TB= ?
16) bisects at point O.DG CT
D
C
O
T
G
CO = 2x + 1OT = x + 7CT = ?
Points, Lines and Planes
