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. Vocabulary Point, line, plane, collinear, coplanar, space, segment, ray, opposite ray, midpoint, congruent, bisects.
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1.1 Points, Lines, and Planes - Coral Gables Senior High · 2015. 8. 18. · x x y z t plane ZYX plane XYZ •Plane –A flat surface that extends indefinitely –Contains lines and
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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.
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.
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