Lesson (1.3) Points, Lines, and Planes Students will… understand basic terms. understand basic...
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Transcript of Lesson (1.3) Points, Lines, and Planes Students will… understand basic terms. understand basic...
![Page 1: Lesson (1.3) Points, Lines, and Planes Students will… understand basic terms. understand basic postulates of geometry. Evidence Outcome: Students will.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfcf1a28abf838ca9bd3/html5/thumbnails/1.jpg)
Lesson (1.3) Points, Lines, and PlanesLesson (1.3) Points, Lines, and Planes
Students will…• understand basic terms. • understand basic postulates of geometry.
Evidence Outcome: Students will express properties with equations (coordinate geometry). (HS 4.3a)
Purpose: Photographers and surveyors use a tripod or a three-legged stand for their instrument.
![Page 2: Lesson (1.3) Points, Lines, and Planes Students will… understand basic terms. understand basic postulates of geometry. Evidence Outcome: Students will.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfcf1a28abf838ca9bd3/html5/thumbnails/2.jpg)
Terms
A point is a location. It does not have a size.Space is the set of all points.
A line is a series of points going in two opposite directions. You can name a line by any two points on the line.Points that lie on the same line are collinear (opposite: noncollinear).
A
BName: AB or BA
![Page 3: Lesson (1.3) Points, Lines, and Planes Students will… understand basic terms. understand basic postulates of geometry. Evidence Outcome: Students will.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfcf1a28abf838ca9bd3/html5/thumbnails/3.jpg)
A
B
C
Terms
A plane is a surface that has no thickness. It contains many lines going in all directions. A plane is named by one capital letter or at least three of its noncollinear points.
Points and lines in the same plane are coplanar.
Names:
P
Plane P Plane ABC or Plane BCA
![Page 4: Lesson (1.3) Points, Lines, and Planes Students will… understand basic terms. understand basic postulates of geometry. Evidence Outcome: Students will.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfcf1a28abf838ca9bd3/html5/thumbnails/4.jpg)
cPostulates/Axioms
A postulate or axiom is an accepted statement of fact.
Postulate 1-1
Through any two points there is exactly one line.
Line t is the only line that passes through points A and B.
A B
Postulate 1-2
If two lines intersect, then they intersect in exactly one point.
AE and BD intersect at C. A C B
D E
![Page 5: Lesson (1.3) Points, Lines, and Planes Students will… understand basic terms. understand basic postulates of geometry. Evidence Outcome: Students will.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfcf1a28abf838ca9bd3/html5/thumbnails/5.jpg)
cPostulates/Axioms
A postulate or axiom is an accepted statement of fact.
Postulate 1-3
If two planes intersect, then they intersect in exactly one line.
Postulate 1-4
Through any three noncollinear points, there is exactly one plane.
Plane RST and Plane STW intersect in ST. R
W
S
T
![Page 6: Lesson (1.3) Points, Lines, and Planes Students will… understand basic terms. understand basic postulates of geometry. Evidence Outcome: Students will.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfcf1a28abf838ca9bd3/html5/thumbnails/6.jpg)
cTry these…
1. Identify collinear points in the room.
2. Identify a plane.
3. Find the intersection of two planes.
4. Draw a plane through three noncollinear points.
![Page 7: Lesson (1.3) Points, Lines, and Planes Students will… understand basic terms. understand basic postulates of geometry. Evidence Outcome: Students will.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfcf1a28abf838ca9bd3/html5/thumbnails/7.jpg)
Lesson (1.4) Segments, Rays, Lesson (1.4) Segments, Rays, Parallel Lines and PlanesParallel Lines and Planes
Students will…• identify segments and rays.• recognize parallel lines.
Evidence Outcome: Students will express properties with equations (coordinate geometry). (HS 4.3a)
Purpose (Relevancy): On a compass, the directions north and south can be represented by opposite rays.
![Page 8: Lesson (1.3) Points, Lines, and Planes Students will… understand basic terms. understand basic postulates of geometry. Evidence Outcome: Students will.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfcf1a28abf838ca9bd3/html5/thumbnails/8.jpg)
Terms
A segment is the part of a line consisting of two endpoints and the points between them.
A B
A ray is one endpoint and all of the points on one side of the endpoint.
Opposite rays are two collinear rays with the same endpoint. Opposite rays always form a line.
![Page 9: Lesson (1.3) Points, Lines, and Planes Students will… understand basic terms. understand basic postulates of geometry. Evidence Outcome: Students will.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfcf1a28abf838ca9bd3/html5/thumbnails/9.jpg)
Naming
Name the segments and rays.
A
BB
C
Three segments:
Four rays:
![Page 10: Lesson (1.3) Points, Lines, and Planes Students will… understand basic terms. understand basic postulates of geometry. Evidence Outcome: Students will.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfcf1a28abf838ca9bd3/html5/thumbnails/10.jpg)
Parallel… ??
•Visualize a plane (it’s flat).•Think of two lines that are both in the plane. •Now make sure that the two lines do not intersect. [PARALLEL]•Notice that the lines are coplanar (in the same plane).
•Now start over with a blank plane.•Think of one line in the plane.•Think of another line that can’t be included in the plane, even if you rotated the plane (remember: the plane has to be flat – it can’t turn a corner).•Now make sure that those two lines do not intersect.•This is different than parallel because the lines are noncoplanar (not in the same plane).
![Page 11: Lesson (1.3) Points, Lines, and Planes Students will… understand basic terms. understand basic postulates of geometry. Evidence Outcome: Students will.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfcf1a28abf838ca9bd3/html5/thumbnails/11.jpg)
Terms
Parallel lines are coplanar lines that do not intersect.
Skew lines are noncoplanar; therefore, we can’t say they’re parallel, but we can say that they do not intersect.
Do skew lines “look” parallel?
![Page 12: Lesson (1.3) Points, Lines, and Planes Students will… understand basic terms. understand basic postulates of geometry. Evidence Outcome: Students will.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bfcf1a28abf838ca9bd3/html5/thumbnails/12.jpg)
Terms
Parallel planes are planes that do not intersect.
*Note: A line and a plane that do not intersect with each other are also parallel.
Example: 1. Identify two parallel planes. 2. Identify a plane and a line that are parallel.
A
B
C
D
J
G H
I