Name the parts of the pyramid shown at the right. all pairs of intersecting planes

Name: Problem 28, Chapter 4: Geometry: Concepts and Applications
Uploaded: 2021-01-04T05:43:41-08:00
Duration: 5 min 34 s
Channel: Anthony Ramos
Description: Name the parts of the pyramid shown at the right. all pairs of intersecting planes

step 1 a square pyramid to be exact. And here on red are named the vertices of this proof. So we got he

Name the parts of the pyramid shown at the right. all pairs...

Key Concepts

Pyramid

A pyramid is a three-dimensional solid that consists of a polygonal base and triangular lateral faces that converge at a single point known as the apex. This geometric figure is fundamental in solid geometry and helps illustrate principles such as symmetry, volume, and surface area.

Plane

A plane is a flat, two-dimensional surface that extends infinitely in all directions. In the study of solids like pyramids, each face of the pyramid is considered a portion of a plane, which is crucial for understanding how these faces interact and intersect.

Intersecting Planes

When two planes meet, they typically intersect along a line. In a pyramid, the edges are the lines of intersection between the planes that form the faces, making it important to analyze these intersections to fully describe the pyramid’s structure.

Edges and Faces

Edges are the line segments where two planar faces meet, and faces are the flat surfaces that bound a solid. Naming and understanding these parts are key to exploring how the individual planes (faces) of a pyramid come together to form its overall shape.

Transcript

00:01 A square pyramid to be exact.

00:03 And here on red are named the vertices of this proof.

00:11 So we got here the a, here is b, c, d and p labels for the vertices.

00:21 And the question is how many planes are determined by these verses? so the first are the trivial planes, the arch, the trivial planes, that are determined by these verses that corresponds to those that form this pyramid.

00:43 So for example, here we can name this plane, this front plane here that is formed by abp, that corresponds to this face here that is in front of the pyramid.

01:04 Then we can put this one so this is constructed by bcp okay the one behind of the pyramid that is formed by dcp the one that is on the left of this pyramid that is constructed by a dp and finally the one that is below so this is a so here below, so let me just erase this part.

01:46 Okay, so this plane here below is, well, actually had four verses, but with three verses is enough to construct this plane.

01:58 So we can choose a, b, c, or actually we can choose adc or any combination of these three verses.

02:11 And it doesn't matter because it corresponds to the same plane.

02:15 Okay, so a, b, c.

02:18 And actually we can say that these are the enough planes that can be formed by these verses.

02:24 However, we are just focusing on the pyramid.

02:27 And the question is how many planes can be determined by these verses.

02:33 So there is some planes that we are not taking into account and are those that intersect the plane.

02:41 So let's visualize this manner.

02:47 So let me raise here this.

02:50 D.

02:51 So actually you can take this plane, like the diagonal inside this pyramid and we got another plane.

03:02 And this plane, as you can see, is formed by b, the b.

03:08 So it's another combination.

03:10 And the same happened on the other side, in the other way...

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