hey it's Kaeleigh in this lesson we will go over the basic definitions and
characteristics of triangles and quadrilaterals let's get started a
triangle is a shape with three sides and three angles we can name our angles
angle B a/c angle ABC and angle a C B and it is made up of three line segments
which we can name a B BC and AC where the line segments intersect is called a
vertex we can name the vertices by the points point a point B and Point C
remember that we can classify triangles by their angles like a right triangle
where one angle is 90 degrees or an acute triangle where every angle is less
than 90 degrees or an obtuse triangle where one angle is larger than 90
degrees but we can also classify triangles by their sides an equilateral
triangle has side lengths that are all the same a scalene triangle has no equal
side links and an isosceles triangle has two equal side links but regardless of
what type of triangle we're working with one thing is always true they have the
same sum of their interior angles interior angles are the angles that are
made at the vertices and a triangle when we add all of these angles together the
Sun is a hundred and eighty degrees for example in an equilateral triangle
all of the angles are the same and if we add them all up we get 60 plus 60 plus
60 which is the same as 60 times three which is a hundred and eighty degrees so
here I have a triangle with two given angles and one mystery angle how will I
find the degrees of my mystery angle well I know that my interior angles are
all gonna add up to 180 degrees so I can say 180 degrees is equal to my mystery
angle plus 70 degrees plus 70 degrees and now I just need to solve this
equation for x so first I'm going to add my known angles 70 plus 70 that's gonna
give me a hundred and forty degrees so now I have a hundred and eighty degrees
is equal to my mystery degrees plus a hundred and forty degrees so if I solve
this for X I'm going to subtract 140 degrees from this side that gives me
zero and 140 degrees from this side which gives me 0 and 4 and 0
forty degrees so my mystery degree is forty degrees a quadrilateral is a shape
with four sides and four angles a quadrilateral has four angles named ACD
b a c c d b and d ba a quadrilateral has four sides made up by line segments that
we can name using the endpoints a b a c BD and CD where the line segments
intersect is called the vertex we name the vertices as points a b c and d
there are many different types of quadrilaterals but they all have four
sides and four angles when you look at this
square what do you notice about line segments a B and C D well there are two
things one they are parallel line segments they are equidistant apart and
will never cross each other and two since you know this is a square that
means that my side lengths are the exact same that means that line segments a B
and C D are congruent congruent is a very important word in geometry it means
two things that are exactly the same shape and size this parallelogram also
has the opposite sides that are congruent line segments a b and c d are
exactly the same shape and size here are five quadrilaterals looking at these
shapes which ones have two sets or two pairs of parallel sides which ones have
four congruent sides remember congruent means line segments that are exact same
shape and size which ones have two sets of congruent sides which ones have one
set of congruent sides while these shapes may all look different they all
have a few things in common besides four angles in the same interior angle some
we will use a square to calculate the interior angle for all quadrilaterals
remember a square has four right angles do you remember the degrees that are
right-angled yeah it's 90 degrees so to find the sum of the interior angles we
would add 90 plus 90 plus 90 plus 90 and this is the same as saying four times 90
which is equal to 360 degrees in this square we can also drive draw a diagonal
line from one vertex to another vertex it's not next to it now we have two
triangles remember each triangle has a sum of interior angles of a hundred and
eighty degrees so if we add the interior angles for both triangles together what
do we get 180 plus 180 which is equal to 360 and we expect that because 360 is
the sum of the interior angles of a quadrilateral so now I have a
quadrilateral with three given angles and one mystery angle how will I find my
mystery angle well I know the sum of all of my interior angles will be 360
degrees so I can say 360 degrees is equal to my mystery angle plus 105
degrees plus 75 degrees plus 75 degrees and I need to solve for my mystery angle
X so let's add up the angles that I know I know 75 plus 75 is 150 degrees and 150
plus 105 is gonna give me 255 so now I have 360 degrees is equal to mystery
angle plus 255 degrees so now if I subtract 255 from either side I'm gonna
get I need to borrow here
501 I get my mystery angle is equal to 105 degrees nice work
great job studying triangles quadrilaterals and their interior angles
you're really getting the hang of geometry now study what you've learned
by doing the online games and quizzes have fun and remember to always be
clever