Transcript Using Triangles to Examine Quadrilaterals

 Given any quadrilateral, if
you were to draw a line from
one of its vertex to another
non-adjacent vertex, this line
or diagonal, will separate the
quadrilateral into two
triangles.
The diagonal.
Here the diagonal separates
the quadrilateral into two
triangles.
 The sum of the measures of the
angles of a triangle is 180 degrees.
 Because all quadrilaterals are
made up of two triangles, the sum
of the measures of the angles in
the quadrilateral will be 360
degrees.
100o
75o
xo
130o
Given the measures of the
angles of the quadrilateral
above, what is the measure of
the angle x?
 Remember that the sum of
the measures of the angles
of the quadrilateral will add
up to 360 degrees because
the quadrilateral is made up
of two triangles.
The measure of the
angles must add up to
360 degrees.
Simplify and solve for x.
The unknown angle must be
equal to 55 degrees.
 If a diagonal separates the
quadrilateral into two identical
triangles, then the quadrilateral
can be classified as a
parallelogram, which means
that both pairs of opposite
sides are parallel and
congruent.