## IS A SQUARE A RECTANGLE? YES OR NO?

[Music]

hello hello everyone and thank you so

much I'm so excited that you're joining

me on this lesson where we get to

explore the question is ask we're also a

rectangle so let's tackle this problem

using an analogy and we'll start out

with the definition of a cookie which is

defined as a small baked treat typically

round flat and crisp and this definition

certainly applies to the oreo cookie

which happens to be one of my favorites

oh yeah so now I want you to think about

the question is every cookie in Oreo and

our answer of course is no we should

know that there are many different kinds

of cookies that satisfied our definition

that in Oreo is a special kind of cookie

and that every Oreo is a cookie but not

every cookie is an Oreo so believe it or

not we just engaged in mathematical

reasoning and now we're going to take

that same kind of thinking and apply it

to our original question is a square a

rectangle so let's go ahead and start

off with the definition of a rectangle

which is a four-sided figure with four

right angles and again we want to see if

a square will satisfy this definition

and allow us to answer the question is

every square a rectangle now we are all

familiar with squares and rectangles and

we can easily draw four-sided figures

with four right angles that would be

considered rectangles and satisfy our

definition I'm sure that you can also

identify four-sided figures that are not

rectangles namely a parallelogram or a

trapezoid because they do not have four

right angles

now remember since the square satisfied

the definition of a rectangle we can say

that a square is a special kind of

rectangle and what makes it special is

not the fact that it has four right

angles but the fact that it has four

equal sides so all the sides are

congruent so if you knew that one side

of a square was five you would know that

all the sides must be five so we can

conclude that every square is a

rectangle but not every rectangle is a

square so when you're asking yourself

this question and you have a figure like

the one shown if it has four right

angles and four sides then you can

conclude that the figure is a rectangle

and if those four sides are all the same

length then you can also conclude that

the figure is a square remember that a

square is a special kind of a rectangle

but also remember that not every

rectangle is a square if we extend our

figure and double the length from five

to ten it still represents a rectangle

but this is not a square again because

the side lengths are not the same and

that is it for this lesson thank you so

much for joining us here at mashup math

we definitely teach things a little bit

more creatively and from a different

perspective we like to be colorful and

fun so we hope that you enjoyed it and

we hope that we got you thinking about

this topic in a different way and we

will catch all of you next time please

stop again soon and have a good one see

ya oh yeah

all right everyone that was it for that

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