hey it's Kaeleigh in this lesson we will be talking about polygons and how to
classify them in our previous lessons we have learned about triangles and
quadrilaterals these shapes are polygons but what makes them a polygon polygons
are closed figures with three or more line segments these shapes are all
examples of polygons notice that all of these are closed figures that means that
all the sides are attached at a vertex and they all have three or more line
segments or sides these figures are not polygons the red and blue shapes have
curved lines polygons do not have curved lines the yellow figure has lines that
intersect or cross each other polygons do not have lines that overlap and the
outline of the green figure is not closed notice that the lines are not
connected at a vertex here are some common polygons with three sides all the
way up to ten sides here is a triangle where a tri means three and a
quadrilateral where quad means four a Pentagon where pent means five and a
hexagon where hex means six a heptagon where hepped means seven and an octagon
where oct means eight a nonagon where non means nine in a decagon where dec
means ten there are two types of polygons regular and irregular regular
polygons are equilateral and equiangular equilateral means that all of the sides
are congruent they are the same shape and size and equal angular means all the
angles are congruent they are all the same measure of degrees the equilateral
triangle is a regular polygon all three sides are the same length and all three
angles are 60 degrees this octagon it's also a regular polygon all eight
sides are the same length and the eight angles are all 135 degrees ear regular
polygons have sides that are not congruent that means they have side
links that are not all the same length they are also not equal angular while
some angles and sides might be the same size and shape not all will be congruent
this parallelogram is an irregular polygon it doesn't have four congruent
sides and angles and this hexagon is an irregular polygon as you can see the six
sides are definitely not all the same length we can draw diagonals in polygons
to help us find the sum of interior angles remember a diagonal is a line
that is drawn from one vertex to another vertex that is non consecutive are not a
neighboring vertex so in this rectangle if I start my diagonal at this vertex
the only other vertex I can draw my diagonal to is this one here now let's
practice drawing diagonals in a polygon with more sides here I have a one two
three four five six sided polygon so a hexagon and I'm going to pick one vertex
to draw my diagonals from we'll use this top line here now I can draw a diagonal
to this vertex here because it's not a neighbor and two this one here and two
this one here but I can't draw to these two vertices because they're neighbors
do you notice anything special about the shapes these diagonals making our
hexagons yeah that's right they're triangles how many triangles can you
count 1 2 3 4 do you remember what the sum of the interior angles for a
triangle is that's right a triangle has a hundred and eighty degrees so if these
each of these triangles has 180 degrees then the sum of the interior angles for
all four triangles would be 180 plus 180 plus 180
180 or 180 times four which gives us 720 degrees and since four triangles fit
inside my hexagon I can say the sum of the interior angles of a hexagon is also
720 degrees let's try another one here I have a heptagon how many sides
seven now let's draw some diagonals from my top vertex now do you see some
triangles again how many one two three four five so now with my heptagon what
would be a very good way to find the sum of the interior angles well if I have
five triangles and I know each triangle is 180 degrees I can just add those up
or say a hundred and eighty times five which is 900 degrees
if it feels time-consuming to draw all those diagonals let's learn another
method here is a table that shows polygons with different number of sides
how many triangles can you fit inside do you notice any patterns between the
number of sides and the number of triangles that will fit inside a polygon
yeah it's always to fewer triangles than sides based on our pattern how many
triangles would fit in a decagon that's right
eight triangles would fit inside a 10 sided shape we can write a formula to
help us we will say the number of sides minus 2 equals the number of triangles
and we can call the number of sides X now here I have an ear regular how many
sides one two three four five six seven eight
so it's an octagon with eight sides so without drawing diagonals how many
triangles can I fit inside remembered number of sides X minus 2 equals number
of triangles and if X I know is 8 minus 2 that'll be 6 triangles will fit inside
and if I know that I have 6 triangles then I can say 6 times a hundred and
eighty degrees will be the sum of my interior angles let's see so 180 times
six I'm gonna go 6 times 8 48 6 that gives
me 10 I bring my extra 0 down so the sum of my interior angles is 1080 degrees
for this octagon so if these are my two formulas X minus 2 or number of sides
minus 2 equals number of triangles and number of triangles times 180 degrees
equals the sum of the interior angles I can plug in X minus 2 into the number of
triangles in my second equation and that will give me X minus 2 times 180 degrees
equals the sum of interior angles so all I need to know is the number of sides on
my polygon and I can calculate the sum of the interior angles great work
studying polygons practice what you've learned by playing the online games and
quizzes have fun and remember to always be clever