1-2 points, lines, and planes. undefined terms term descriptionhow to name itdiagram point:...
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1-2 Points, Lines,
and Planes
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Undefined TermsTerm Description How to Name it Diagram
Point: indicates a location and has no size
Point AOR A
Line: represented by a straight path that extends in two opposite directions without end and has no thickness. A line contains infinitely many points
Name a line by any two points on the line: or
Or by a single lowercase letter such as line m
Plane: represents a flat surface that extends without end and has no thickness. A plane contains infinitely many lines
Name a plane by a capital letter, such as plane P
Or by at least three points in the plane that do not lie on the same line, such as plane ABC
AB
m
P
C
B
A
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Collinear Points: Points that lie on the same line
Coplanar: Points and lines that lie in the same plane
All points of a line are coplanar!
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Problem 1: Naming Points, Lines, and Planes
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Defined TermsTerm Description How to Name it Diagram
Segment: part of a line that consists of two endpoints and all the points between them
Name a segment by its two endpoints: or
Ray: part of a line that consists of one endpoint and all the points of the line on one side of the endpoint
Name a ray by its endpoint and another point on the ray: (read “ray AB”). The order of the points indicates the ray’s direction
Opposite Rays: two rays that share the same endpoint and form a line
Name opposite rays by their shared endpoint and any other point on each ray:
AB
CB
A
AB
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Problem 2: Naming Segments and Rays
• What are the names of the segments?
• What are the names of the rays?
• Which of the rays are opposite rays?
• Are opposite rays?
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DAY 2:
Points, Lines, and Planes Continued
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Problem 3: Finding the intersections of Two Planes
Postulate (axiom): an accepted statement of fact. They are basic building blocks of the logical system in geometry (to prove general concepts)
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Side note: when you know two points that two planes have in common, Postulate 1-1 and 1-3 tell you that the line through those points is the intersection of the planes.
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Each surface of the box represents part of a plane. What is the intersection of plane ADC and plane BFG?
When you name a plane from a figure like this box, list the corner points in consecutive order. EX: plane ABCD and plane ADCB are names for the top plane but plane ACBD is not!!
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• What are the names of the two planes that intersect in ?
• Why do you only need to find two common points to name the intersection of two distinct planes?
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Problem 4: Using Postulate 1-4
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•What plane contains points N, P, and Q? Shade the region.
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•What plane contains points J, M and Q? Shade the region.
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•What plane contains points L, M and N? Shade the region.
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•What is the name of a line that is coplanar with ?