WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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For the next lesson, we are going to go over prisms and cylinders.
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A prism is the first type of polyhedron or solid that we are going to go over.
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Polyhedron, that sounds like a big word; but poly means many.
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We are used to hearing the word polygon.
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Polygon remember is like a shape where we have many sides; polygon.
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Polyhedron, it is a way of saying many faces.
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We are going to go over face in a bit.
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But polyhedron is just when you have a three-dimensional figure, three-dimensional object.
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Each side has to be straight; it has to be a segment.
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That is called a polyhedron.
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Another name for these three-dimensional objects are called solids.
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Solids, we can have round or circular sides.
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But polyhedrons, that is the only difference between them.
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They are pretty much the same thing.
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Solids and polyhedron, they are both talking about three-dimensional objects.
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Solids, they could be circles; the sides could be circles.
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For polyhedrons, each side has to be straight.
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They have to be segments, line segments; many faces.
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Prism is the first type.
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Prism is when you have a three-dimensional object with two opposite faces that are parallel and congruent.
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It is talking about faces.
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Each one of these sides like this right here, this right here, and this right here, those are all faces.
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All the sides of the prism, the three-dimensional solid, is a face.
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When two of those faces are parallel and congruent, the two opposite faces are parallel and congruent,
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then you have what is called a prism.
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Those two faces that are parallel and congruent, those two are called bases.
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This base, we can label as the top face and the bottom face.
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You can't really see a bottom face.
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Those can be labeled as bases because see how these two sides are congruent and they are parallel.
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So those could be labeled as bases.
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Anytime you have just two opposite faces being parallel and congruent, you have a prism.
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This is called a rectangular prism because the bases are rectangles.
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You are probably thinking that these two sides, the left and the right side, are also parallel and congruent.
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The front and the back sides, this front and the back, are also parallel and congruent.
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Rectangular prisms, you can actually label any two opposite faces as your bases.
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Let me give you an example of one that is not rectangular prism.
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Say I have two, three, four, five; and then I have...
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When I have something like this, this is also a prism.
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The bases would be this top face and this bottom face because they are both parallel and congruent.
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This is called a prism; more specifically what is the base in the shape of?
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What is the polygon?--this is a pentagon.
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This is actually called a pentagonal prism because the base is in the shape of a pentagon; five sides.
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Another example would be triangle; let's say... like that.
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The bases are not going to be top and bottom.
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In this case, it doesn't have to be top and bottom.
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There is nowhere where it says the bases of the prism has to be top and bottom.
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As long as the two faces that are opposite are both parallel and congruent.
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Meaning they are facing the same direction; they are not going to ever intersect.
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They are congruent; they have to be exactly the same.
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This is also a prism because we do have two sides that are parallel and congruent.
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This, the base is in the shape of a triangle.
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This is a called a triangular prism; these are prisms.
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We are pretty much only going to go over the rectangular prism.
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But just so you understand what a prism is, these are just a few examples.
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Again this is called base; prisms always have two bases.
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We have to have two bases.
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The rest of the sides, the rest of the faces, the ones that are not bases, are called lateral faces.
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This right here, this right here, this side right here,
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this backside right here, those are all lateral faces.
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This is a lateral face, lateral face, lateral face.
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This triangle is a lateral face; those are all lateral faces.
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All the sides of a prism are either considered bases or lateral faces.
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Regular prism; regular we know is when all the sides are the same.
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It is regular; all the sides are the same; all the faces are the same.
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That is what it means for a prism.
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If I have a regular prism, that means all the faces are exactly the same.
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They are all congruent.
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If I have a rectangular prism where all the sides are the same,
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then we know that each side has to be a square.
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Each side of this is congruent.
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This, the name for this, there is a specific name; it is a cube.
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I am sure you heard of that before; cube.
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A cube is a rectangular prism that is regular; regular prism.
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We went over base; we went over faces; each side is a face.
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This right here, each of these segments are called...
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let me just draw this base to this base so you know that that is what I am talking about.
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Each of these sides, these segments, they are called edges.
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Edge there; this is an edge; this is an edge.
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All of those are called edges; sides are faces; these are edges.
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This right here is like the vertex; but the plural word for vertex is vertices.
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All of these make up the vertices of a prism.
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We have base or another face.
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Because each one of these are faces, more specifically, this is a base.
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But these are all considered faces, edges, and vertices.
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The next type of solid is a cylinder; you have seen the shape before.
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Maybe a can of soup; that is a cylinder.
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Lot of things; a cup could be a cylinder.
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A cylinder is when we have two bases that are congruent and parallel circles.
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It is almost the same thing as a prism where we have two opposite faces being parallel and congruent.
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With the bases, they are called bases.
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But in this case, the two bases have to be circles.
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If they are circles, then it is a cylinder.
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We know that this is a base and this has to be the base.
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Those are circles; the altitude is like the height.
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A height is how tall this is; how tall is it standing; this is H.
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If you lay it down sideways so it is like this, make sure that this has to be the height.
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It is from base to base; that is considered the height.
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Again cylinder is a solid where we have two circles as the bases and this is the height.
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The altitude is the height.
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Our first example is classifying each prism by the shape of its bases.
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This first one, it is almost the same as the one that we went over.
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The base for this, it has a few different pairs that we can label as bases.
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But you can't label all of them as bases.
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Only two faces can be the bases; two faces can be bases.
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If you want, you can label the top and the bottom as bases.
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Or if you want, you can label the front and the back.
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Or the left and the right sides; as long as it is only two sides.
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But make sure it is not top and like left.
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They have to be opposite sides; it has to be congruent.
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I want to label my top and my bottom as my bases.
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Figure out this shape of the base; it is a rectangle.
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It is in the shape of a rectangle; this would be a rectangular prism.
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The next one, here if you look at this side right here, the left side,
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left side and right side, see how they are intersecting right here.
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They can't be called the bases.
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Even though they are the same, they are congruent,
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they are not parallel because they are intersecting.
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The bottom side, this rectangle right here, is not parallel and congruent with any other side.
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So it has to be this triangle here; this triangle, this front and this back.
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Those would be the two bases; again parallel and congruent.
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That is in the shape of a triangle; the base in the shape of a triangle.
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This is called triangular prism.
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Then the third one, here even though...
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This one is a little bit tricky because we do have opposite sides being parallel and congruent.
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But they can't be... the lateral faces... I forgot to mention this to you guys.
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But lateral faces, meaning the sides that are not bases, they have to be rectangular.
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This top and this bottom are the only sides that are not rectangular.
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They are not rectangles; they have to be the bases.
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If you are having a difficult time identifying what sides are the bases,
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just look for the sides that are not rectangles.
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Look for the sides that are not rectangles.
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You should look at this side, the top side and the bottom side, because they are not rectangles.
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Let's say those two are not parallel and congruent.
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Then it wouldn't be considered a prism; it is not a prism.
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This with this bottom side are the bases.
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This shape, one, two, three, four, five, six.
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Remember a polygon with six sides is a hexagon.
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This is a hexagonal; I just put a ?al; hexagonal prism.
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That is the name for this right here; they are all prisms.
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This is a rectangular prism; triangular prism; hexagonal prism; based on the shape of its bases.
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Next example, name two different edges, bases, and vertices of the prism.
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Remember what edges are, bases are, and vertices are.
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Edges are like the edges of this prism, the segments.
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Two different edges; AC and DE or ED.
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It doesn't matter because either way you go from here to here.
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Or here to here, it is the same thing.
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I can say BE; any one of these edges, you can name.
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Faces... I am going to use a different color; faces.
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Faces, any one of these faces; I can say CDBE; this is a rectangle.
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I can say rectangle CDEB; or I can say triangle ACB.
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If you recognize that this is also the base.
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But remember all these sides are just called faces.
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Face is another word for saying sides; face.
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The last one, vertices; vertices, think of vertex, those points right there.
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I can say point B; point E; those are vertices.
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The third example, name the solid for each object.
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We are going to see what shape, what the name of the solid is for each of these.
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The first one, a can of soup.
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We know a can of soup looks like this; this will be cylinder.
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A shoebox, we know that a shoebox is in the shape of a prism.
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More specifically, it would be a rectangular prism.
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Camping tent; this one...
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I am just going to draw it out for you guys so you guys can see a little bit better.
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Yes, there is different versions of camping tents.
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But this main one like this if you can see that... horrible at drawing... like that.
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This would be... look at the bases; the bases are triangles.
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This is a triangular prism.
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A roll of paper towels; paper towels, it looks like this.
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It has that, a little bit longer; it has the hole in the middle; like that.
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This one would be cylinder.
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The fourth example, we are going to write true or false for each statement.
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The first one, a cylinder has congruent bases.
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Cylinder, we know it must have congruent bases.
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Or else it is not going to be called a cylinder.
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The bases are congruent circles; so this is true.
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A triangular prism has three faces; triangular prism, like this; does it have three faces?
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Just the front and the back, this right here, just the bases alone, there is two.
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But then you have to think that there is this side; that is three.
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The other side which is this, this other side, that is four.
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Then the bottom side, that is five; each one of those is faces.
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Does it have three face?--no; this one is false.
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A cube is a rectangular prism.
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Remember a cube is a regular prism where all the sides are the same.
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There is a cube; is it a rectangular prism?
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Are the bases in the shape of rectangles?
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It is actually in the shape of squares.
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But isn't a square a type of rectangle?
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So this one is true; cube is a rectangular prism.
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That is it for this lesson; thank you for watching Educator.com.