1.2 Points, Lines, and Planes
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Transcript of 1.2 Points, Lines, and Planes
What is a definition?What is a definition?
Known words used to describe a new wordKnown words used to describe a new word
Undefined termsUndefined terms – are terms not formally – are terms not formally defined.defined.
There are three undefined terms in geometry: There are three undefined terms in geometry:
1. Point1. Point 2. Line2. Line 3. Plane3. Plane
PointPoint
1. A location in space.1. A location in space.
2. Has no dimension (no length, no width, no 2. Has no dimension (no length, no width, no depth). depth).
3. Usually represented by a dot.3. Usually represented by a dot.
4. Named using one capital letter. 4. Named using one capital letter.
LineLine
1.1. A series of points that extends in opposite A series of points that extends in opposite directions without end. directions without end.
2.2. One-dimensional (length).One-dimensional (length).
3.3. Has an arrowhead on each end Has an arrowhead on each end representing the fact that it goes on representing the fact that it goes on forever. forever.
4.4. Always straight.Always straight.
5.5. Named with a lowercase script letter or by Named with a lowercase script letter or by 2 points on the line2 points on the line
LineLine
AA BB
ll
Can be called:Can be called:
Line Line ll
Line AB or ABLine AB or AB
Line BA or BALine BA or BA
For example:For example:
PlanePlane
1.1. A flat surface that extends forever in two A flat surface that extends forever in two dimensions (length & width).dimensions (length & width).
2.2. Contains infinitely many points and lines.Contains infinitely many points and lines.
3.3. Usually represented by a four-sided Usually represented by a four-sided figure.figure.
4.4. Named with a capital script letter or 3 Named with a capital script letter or 3 points on the surface of the planepoints on the surface of the plane
PlanePlane
AA
BC
W Can be named:Can be named:
Plane Plane WW
Plane ABC, plane BCA, plane Plane ABC, plane BCA, plane CBA, etc.CBA, etc.
For example:For example:
More DefinitionsMore Definitions
Collinear points –Collinear points –
points that points that cancan lie on the lie on the same line.same line.
More DefinitionsMore Definitions
Coplanar points – Coplanar points –
points that points that cancan lie on the same plane. lie on the same plane.
More DefinitionsMore Definitions
IntersectIntersect – –
Two or more figures intersect if they Two or more figures intersect if they have one or more points in common.have one or more points in common.
IntersectionIntersection – –
All points or sets of points the All points or sets of points the figures have in common.figures have in common.
When a line and a point intersect, When a line and a point intersect, their intersection is a point.their intersection is a point.
BB
ll
When 2 lines intersect, their When 2 lines intersect, their intersection is a point.intersection is a point.
When 2 planes intersect, their When 2 planes intersect, their intersection is a line.intersection is a line.
When a line and plane intersect, their When a line and plane intersect, their intersection is a point.intersection is a point.
Horizontal Planes – Ceiling and Floor
Horizontal Planes – Two sides horizontal and no sides vertical
Group Practice
Point P is not in Plane N. Three lines through point P intersect N in points A, B, and C.