Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.
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Transcript of Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.
![Page 1: Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.](https://reader034.fdocuments.in/reader034/viewer/2022051215/56649d965503460f94a7eb43/html5/thumbnails/1.jpg)
Points, Lines, and Planes
SY 2015-2016
Reference: Geometry (2007) by Ron Larson et al
![Page 2: Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.](https://reader034.fdocuments.in/reader034/viewer/2022051215/56649d965503460f94a7eb43/html5/thumbnails/2.jpg)
Undefined Terms
O POINT - basic unit of Geometry- has location- has no size
![Page 3: Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.](https://reader034.fdocuments.in/reader034/viewer/2022051215/56649d965503460f94a7eb43/html5/thumbnails/3.jpg)
Undefined Terms
O LINE- straight array of an infinite number of points
- no exact measure of length- no thickness- extends indefinitely in
opposite directions
![Page 4: Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.](https://reader034.fdocuments.in/reader034/viewer/2022051215/56649d965503460f94a7eb43/html5/thumbnails/4.jpg)
Undefined Terms
O PLANE - described as a flat surface extending indefinitely along its length and width
![Page 5: Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.](https://reader034.fdocuments.in/reader034/viewer/2022051215/56649d965503460f94a7eb43/html5/thumbnails/5.jpg)
Defined Terms
O SPACE - set of all pointsO COLLINEAR – on the same lineO COPLANAR - on the same plane
Collinear points are coplanar. (asn)
Coplanar points are collinear. (asn)
Collinear points are coplanar. (asn)
Coplanar points are collinear. (asn)
![Page 6: Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.](https://reader034.fdocuments.in/reader034/viewer/2022051215/56649d965503460f94a7eb43/html5/thumbnails/6.jpg)
Checking Your Understanding
Let’s interpret the figure!
![Page 7: Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.](https://reader034.fdocuments.in/reader034/viewer/2022051215/56649d965503460f94a7eb43/html5/thumbnails/7.jpg)
Postulates
O Postulate: Through any two points, there exists
exactly one line.
O Postulate:A line contains at least two
points.
![Page 8: Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.](https://reader034.fdocuments.in/reader034/viewer/2022051215/56649d965503460f94a7eb43/html5/thumbnails/8.jpg)
Postulates
O Postulate:If two lines intersect, then their intersection is exactly one point.
![Page 9: Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.](https://reader034.fdocuments.in/reader034/viewer/2022051215/56649d965503460f94a7eb43/html5/thumbnails/9.jpg)
Checking Your Understanding
Let’s interpret the figure!
![Page 10: Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.](https://reader034.fdocuments.in/reader034/viewer/2022051215/56649d965503460f94a7eb43/html5/thumbnails/10.jpg)
Checking Your Understanding
Let’s interpret the figure!
![Page 11: Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.](https://reader034.fdocuments.in/reader034/viewer/2022051215/56649d965503460f94a7eb43/html5/thumbnails/11.jpg)
Postulates
O Postulate: If two planes intersect, then their intersection is a line.
![Page 12: Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.](https://reader034.fdocuments.in/reader034/viewer/2022051215/56649d965503460f94a7eb43/html5/thumbnails/12.jpg)
Checking Your Understanding
Let’s interpret the figure!
![Page 13: Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.](https://reader034.fdocuments.in/reader034/viewer/2022051215/56649d965503460f94a7eb43/html5/thumbnails/13.jpg)
Postulates
O Postulate:Through any three non-collinear points,
there exists exactly one plane.
Through any three collinear points, there exists at least one plane.
![Page 14: Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.](https://reader034.fdocuments.in/reader034/viewer/2022051215/56649d965503460f94a7eb43/html5/thumbnails/14.jpg)
Checking Your Understanding
Let’s interpret the figure!
![Page 15: Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.](https://reader034.fdocuments.in/reader034/viewer/2022051215/56649d965503460f94a7eb43/html5/thumbnails/15.jpg)
Checking Your Understanding
Let’s interpret the figure!
![Page 16: Points, Lines, and Planes SY 2015-2016 Reference: Geometry (2007) by Ron Larson et al.](https://reader034.fdocuments.in/reader034/viewer/2022051215/56649d965503460f94a7eb43/html5/thumbnails/16.jpg)
Checking Your Understanding
Let’s interpret the figure!