ShmoopTube
Where Monty Python meets your 10th grade teacher.
Search Thousands of Shmoop Videos
Plane Geometry Videos 23 videos
ACT Math: Plane Geometry Drill 1, Problem 4. What angle is supplementary to Angle 10?
ACT Math: Plane Geometry Drill 1, Problem 5. If two polygons have the same shape and size, they are what?
Geometric Planes are great and all, but you don't really want to book a flight to Tahiti on one. They're aerodynamic, sure, but good luck finding a...
Geometric Planes 793 Views
Share It!
Description:
Geometric Planes are great and all, but you don't really want to book a flight to Tahiti on one. They're aerodynamic, sure, but good luck finding any leg room.
Transcript
- 00:04
Geometric Planes, a la Shmoop.
- 00:07
It's a bird!
- 00:08
It's a plane!
- 00:09
It's… Shmooperman!
- 00:11
Oh, wait. Our bad. It is a plane.
Full Transcript
- 00:14
A geometric plane.
- 00:16
In geometry, planes are undefined notions, along with points and lines.
- 00:23
It just means that defining them is a bit tricky, but we can still describe them.
- 00:28
Planes have infinite length and infinite width, but no depth at all.
- 00:36
You can think of them as infinitely thin sheets of paper that extend forever in all directions….
- 00:42
…kind of like your mom's collection of wrapping paper around the holidays.
- 00:46
Of course, since we can't draw something that has infinite length and infinite width,
- 00:50
we settle for drawing something like this.
- 00:53
That's plane M.
- 00:55
Just like any two points define a line, any three points can define a plane.
- 01:01
That's the reason tripods don't wobble nearly as much as bipods do.
- 01:05
And that's also why bipods… don't really exist.
- 01:09
So given this figure, which points are NOT on plane M?
- 01:18
If a point is on a plane, we usually draw it within the boundaries of the plane.
- 01:22
These boundaries aren't real, of course, since planes go on forever.
- 01:25
But drawing those boundaries spares our brains from trying to visualize infinity.
- 01:30
The points that are on plane M are H, B, C, D, and F
- 01:35
because they're all contained within the boundaries of M.
- 01:38
That means that the rest of the points… highlighted here for your viewing pleasure...
- 01:42
A, E, and G… are not on plane M.
- 01:46
Which points are both on planes M and N?
- 01:50
As in Mike and Nancy.
- 01:52
For points to be on both planes M and N,
- 01:56
they need to be contained within the boundaries of those planes in the figure.
- 02:02
We can see that points H, B, C, D, and F are on plane M,
- 02:05
and points A, B, C, and D are on plane N, Nancy.
- 02:09
Only points B, C, and D are shared by both those planes. And they're collinear!
- 02:20
Just like two lines intersect at a point, two planes intersect at a line.
- 02:24
Points B, C, and D are on the line that results from the intersection of planes M, Mike, and N, Nancy.
- 02:30
So… while a geometric plane isn’t going to swoop in and catch
- 02:34
you after falling from a 37-story window…
- 02:37
…it’s still pretty… super.
- 02:38
What were you doing that close to the window, anyway?
Related Videos
ACT Math: Plane Geometry Drill 3, Problem 1. What is the area of the trapezoid shape in the video?
ACT Math: Coordinate Geometry Drill 1, Problem 1. Which inequality is expressed by the number line?
ACT Math: Intermediate Algebra: Drill 3, Problem 1. Find the fifth number in the series.
ACT Math Pre-Algebra Drill 2, Problem 5. Given the chart in the video, what is the mode?