Similar Figures and comparison with Congruent Figures Video Lecture - Class 10

hey there everyone welcome back to
mashup math my name is Anthony and thank
you again so much for joining me on this
mini lesson just go ahead and get
started
hey everyone thank you for joining me on
this lesson where we are going to
explore the differences between similar
and congruent so let's start off with
the question what does it mean when two
things are similar so let's start out by
looking at some pairs of everyday items
we could probably describe each of these
pairs as being similar in some way could
be based on shape color species function
or many other ways of describing these
things but when it comes to geometry and
looking at mathematical figures our
definition of similar is much more
specific so let's go ahead and explore
that further by looking at the pair of
shoes notice that despite being
different colors both images have the
same shape and this is still true even
when we change the size by making one
larger or smaller this is also still
true when we change the orientation by
rotating them in one direction or
another so now as we discuss two figures
being similar we are going to focus on
whether or not they have the same shape
so here's another example of two similar
figures the two ghosts are different
sizes but they have the same shape even
if one is facing at different directions
and the other they still have the same
shape
therefore they are still similar now
when we say the same shape we have to be
specific in that the two figures are
proportional to each other and we can
illustrate this by overlapping the two
now from here we can clearly see that
the figures are similar but since they
are not the identical same size we can
also conclude that they are not
congruent so now let's go ahead and
explore
or why now moving forward let's keep the
following exploration questions in mind
how can I be sure that two figures are
similar what is the difference between
similar and congruent can a figure be
both similar and congruent at the same
time and when is that cute ghosts going
to show up again so now let's go ahead
and extend our thinking we have two
figures and we want to describe whether
or not they are similar and/or congruent
to each other starting with similarity
we can see that these are both regular
Pentagon's so since they are the same
shape we can conclude that yes they are
similar to each other and if we can
visualize overlapping the two figures
it's easy to see that taking the smaller
Pentagon and making it larger would make
it identical to the larger purple
Pentagon
therefore they are proportional to each
other we can conclude here that the
figures are similar because they have
the same shape however we can see that
these figures while being similar
clearly are not the same size so we can
also conclude that the figures are not
congruent because they are not the same
size and we can add that both similar
and congruent figures have the same
shape but congruent figures also have
the same size
so let's quickly check out a few more
examples look at the two figures shown
here in terms of them being similar I
can see that they are the same shape and
that they are proportional to each other
so we know that these two figures are
similar however it is very easy to see
that they are not the same size so we
can also conclude that they are not
congruent
let's look at two more figures to see
whether or not they are similar we have
to change the orientation so that
they're both facing in the same
direction which helps us to see that yes
they are the same shape they are both
regular hexagons we can also see by
overlapping the two figures that they
are identical in size so this pair of
figures is both similar and congruent
which leads us to the conclusion that
all congruent figures are similar but
not vice versa meaning that not all
similar figures are congruent and there
is of course the possibility of a
situation where two figures are neither
similar nor congruent to each other can
you imagine what that might look like so
now you should have a better
understanding of the concepts of similar
and congruent figures so keep these in
mind as you continue to explore these
properties and get into some more
advanced problems so thank you again for
checking us out and I'll see you next
time
all right so that's it for this lesson
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next time bye