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 quadrilaterals.
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Remember a quadrilateral is a four-sided figure.
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Any polygon with four sides is a quadrilateral.
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That means the four sides has to be straight sides, and they have to be enclosed.
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This is a type of quadrilateral.
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Any shape that has four straight sides and no open areas is a quadrilateral.
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Special types of quadrilaterals are listed out here.
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The first one is a parallelogram; a parallelogram looks like this.
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It has two pairs of opposite sides being parallel and congruent.
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Again opposite sides are parallel and congruent.
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Parallel means that they are slanted exactly the same way so that they will never touch.
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If this line and this line were to keep going forever and ever, they are never going to touch.
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That is what it means to be parallel; they are also congruent.
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To show two sides are parallel, you can draw arrows like that.
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One arrow with one arrow here shows that those two sides are parallel.
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I can also say that these two lines are congruent.
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I draw two marks like; remember that means they are congruent.
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Then to show that these two sides are parallel and congruent, instead of drawing just one arrow
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because one arrow is for these two, I have to draw now two arrows.
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Now I am saying all the sides with two arrows are parallel to each other.
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To also show that these two sides are congruent, I have to draw two marks instead of just one
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because all the ones with one are congruent so all the ones that have two are congruent.
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This is a parallelogram; again opposite sides are parallel and congruent.
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These two sides are parallel and congruent; these two sides are parallel and congruent.
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That is a parallelogram.
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A type of parallelogram is a rectangle.
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A rectangle is a type of parallelogram because parallelogram just has opposite sides parallel and congruent.
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Rectangle has opposite sides parallel and congruent.
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It is a parallelogram with four right angles.
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It has all the properties of a parallelogram plus it has four right angles.
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Opposite sides are parallel; these are parallel and congruent; parallel and congruent.
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And it has four right angles; it is a special type of parallelogram.
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The next type of parallelogram is a rhombus.
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Rhombus, opposite sides are parallel and congruent; plus it has four congruent sides.
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All sides are sides are congruent.
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Again rhombus is a type of parallelogram.
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It is not a type of rectangle; it is a type of parallelogram.
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This is that; and then parallelogram with rhombus also.
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The next one, square, we know what a square is.
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But square is also a parallelogram.
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But more specifically, it is a type of rectangle and it is a type of rhombus.
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Square is like all of the above; why?
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Not only does it have parallel and congruent sides,
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it also has four right angles and it has four congruent sides.
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The square, it has this one; it has this one; and it has this one.
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That is a square.
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The last one, the trapezoid; trapezoid is not a parallelogram.
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Remember parallelogram has to have both pairs being parallel and congruent.
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Trapezoid only has one pair; that means only this and this one are parallel.
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One pair of parallel sides; that is the only requirement for a trapezoid.
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Only one pair of parallel sides is trapezoid.
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Two pairs of parallel sides and it is a parallelogram; these are obviously not parallel.
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If these two sides were to keep going on forever, then they are going to eventually intersect.
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Or they are going to eventually meet; so this cannot be a parallelogram.
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Let's look at this flowchart; this right here is a parallelogram.
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We have parallel and congruent; these two sides being parallel and congruent.
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This is a parallelogram; there are two types of parallelograms.
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This is a rectangle; this is a rhombus.
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By the way, when you have more than one... rhombus is singular, when you only have one.
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When you have more than one, it becomes rhombi; rhombi is the plural for rhombus.
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Rectangle, rhombus; two types of parallelograms because a property of parallelogram...
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As long as it has two pairs of opposite sides parallel and congruent, then it is a type of parallelogram.
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This one also has that property; this one also has that property.
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This one has to have four right angles; then it is a rectangle.
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This one has all the parallelogram properties; plus it has four congruent sides.
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Four right angles; four same sides.
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Then when you combine all those properties together, it actually becomes this, a square.
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Notice that a square has four right angles.
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And it has four congruent sides, four same sides.
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Square is always a rectangle; a square is always a rhombus.
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So square is always a parallelogram.
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Parallelograms are sometimes going to be rectangles and sometimes going to be rhombi.
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Or it can just be a parallelogram.
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Same thing here; rhombus can be a rhombus; or sometimes it can be a square.
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When you look at this flowchart, if you are going downwards,
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meaning you are comparing a parallelogram let's say to a rectangle, isn't it only sometimes?
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Parallelogram is sometimes a rectangle because it can also be a rhombus.
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When you are going down on the flowchart, it is going to be sometimes.
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When you go up on the flowchart, isn't a rhombus always a parallelogram?
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because the rhombus always has the properties of a parallelogram.
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If you are going up on the flowchart, if you are comparing
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like a rhombus to a parallelogram, a rhombus is always a parallelogram.
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A square is always a rectangle because it always has four right angles.
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A square is always going to be a rectangle; this is always.
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Let's look at let's say a trapezoid.
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A trapezoid doesn't fit anywhere on this flowchart.
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Why?--because it starts off with parallelogram.
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Parallelograms have to have two pairs of parallel sides and congruent sides.
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Trapezoid only has one; so trapezoid goes over here to the side.
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Parallel sides; that is a trapezoid.
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Is a trapezoid ever going to be a parallelogram?--no, they are two different things.
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One pair of parallel sides; two pairs of parallel sides.
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Trapezoid, parallelogram?--never; a trapezoid to a rectangle?--never.
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On the flowchart if you go left or right, how about rectangle with rhombus?
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Are they ever going to be the same?--no, so this is never.
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Again when you are going downwards, it is sometimes.
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It is like classifying let's say animals; let's say quadrilaterals is like animals.
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Parallelograms are types of quadrilaterals; let's say parallelograms are like dogs.
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Parallelograms are like dogs; don't we have different types of dogs?
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We can have Maltese; we can have Chihuahuas.
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We can have whatever, any types of dogs.
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The different types of dogs can go there.
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From there, we can classify even further; that is kind of how it goes.
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If I go as a dog, always, sometimes, never a Maltese; isn't it just sometimes?
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Again when you go downwards, it is sometimes.
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But then again, is a Maltese always, sometimes, never a dog?--isn't it always?
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If I go side by side, it is going to be never.
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Let's say over here where the trapezoid belongs, if I write birds.
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Birds and dogs, they don't have anything to do with each other.
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They are two different things.
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If I ask you when is a bird a dog?--never.
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That is how this flowchart works; this is just an example.
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Let's do our examples; give the most exact name for the figure.
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Here we have four congruent sides; what has four congruent sides?
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We know that a square has four congruent sides.
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But then again square also has to have four right angles.
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This can be a rhombus; this can also be a parallelogram.
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But a more exact name would be rhombus.
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How about this one here?--this looks like a rhombus.
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But I don't know that all four sides are congruent.
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I know that these two are.
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All I can say, because all I notice is that these two are congruent.
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I do have two pairs of parallel sides; so then this is a parallelogram.
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The last one, it looks like a rectangle; but I am not sure.
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Here only one pair of parallel sides.
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I don't see that any of the sides are congruent or the same.
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No, it doesn't seem like any two sides are the same.
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That is all I have; just that it is parallel; one pair.
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This must be a trapezoid.
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Just because it looks like a rectangle, it doesn't mean that it is.
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Looks like maybe this side and this side, they are not parallel.
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This side looks a little bit longer than this side; we can't really assume.
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Just based on the facts, this being parallel to that and that is it, it would be a trapezoid.
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The next one, if a parallelogram has four right angles, then it is a...
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What do we know has four right angles?
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We know a square has four right angles and a rectangle has four right angles.
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But isn't a square a type of rectangle?--then this has to be a rectangle.
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because if I say rectangle, then I am also including squares because a square is a type of rectangle.
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A rhombus is a type of what?--yes, it is a quadrilateral.
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But more specifically, it is a type of parallelogram.
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If a quadrilateral has one pair of parallel sides, then it is a...
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If it is two, then it is a parallelogram; one then it is a trapezoid.
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The next example; always, sometimes, or never.
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Let's see; a trapezoid is always, sometimes, or never a rectangle.
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Remember that example where I said trapezoid is like a bird and a rectangle is a type of dog.
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A bird is never going to be a dog.
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It is going side by side on the flowchart.
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It was trapezoid here; you know let me write it in red.
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The flowchart starts off as quadrilaterals; we have trapezoids here; we have parallelograms here.
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Parallelograms, the two types are rectangles and the rhombus.
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These two have a square; here is your flowchart.
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Again if you are going side by side, meaning if there is no arrows connecting them, then it is never.
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Quadrilaterals is like saying animals.
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Trapezoids is a type of animal; it is like a bird.
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Parallelograms are like dogs; they branch out to the different types.
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We said Chihuahuas and Maltese or whatever you want to say.
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This can be, I don't know, maybe a type of Chihuahua or something.
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That is kind of the idea of the flowchart.
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Trapezoids, the birds, can never be type of a dog; so this is never.
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A rhombus is always, sometimes, never, a parallelogram.
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Maltese is always, sometimes, never, a dog; isn't it always?
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If we are going to go up, then it is always.
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A rectangle is always, sometimes, never a square.
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Rectangles can just be rectangle; sometimes it could be a square.
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Is a square always, sometimes, never a rectangle?
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Because a square is a type of rectangle, it always has to be a rectangle.
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That is it for this lesson; thank you for watching Educator.com.