Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school
Brian was a geometry teacher through the Teach for America program and started the geometry program at his school
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Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school
Brian was a geometry teacher through the Teach for America program and started the geometry program at his school
Properties of parallelograms often show up in geometric proofs and problems. Parallelogram properties apply to rectangles, rhombi and squares. In a parallelogram, opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary and diagonals bisect each other. Other important polygon properties to know are trapezoid properties, and kite properties.
Properties of quadrilaterals show up
all over geometry, in proofs, in
true and false questions, in multiple
choice and fill in the blank. So
it is really good to know the properties of
various quadrilaterals.
Parallelograms have properties that apply to rectangles,
rhombi and squares. So
whatever we decide that parallelograms
have as properties is going to
apply to those three parallelograms
as well.
First key thing is opposite sides are congruent.
Well, if I look at opposite sides,
I'm going to mark those two sides as
being congruent to each other.
But how do we know this is a parallelogram?
Definition of a parallelogram
is that we have two pairs of parallel
sides. So notice in a parallelogram
that all four sides don't need to
be congruent. If they were, that
would be a rhombus.
The second key thing is that the opposite angles
are congruent. So if I look at this
angle right here, it's opposite.
Basically, if I drew a diagonal,
where would that angle be? So
opposite angles are congruent. I will
mark these two angles as being
congruent to each other but not congruent
to the other consecutive angles.
The next thing is consecutive angles
are supplementary. If I call
this angle X and this will be angle
Y. So this will be X and this
will be Y. No matter how I looked at
these consecutive angles, X plus Y,
they are going to equal 180 degrees.
Why is that? If I have
two parallel lines, this side of here
can be thought of as a transversal,
we have same side interior angles which
are always supplementary. Same
can be said for these two parallel
lines where we have a transversal.
So no matter how I look at this, I'm
going to have same side interior
angles.
And the last key thing is
that the diagonals will bisect
each other. So I'm going to draw that
in in a different color marker.
So if I drew in a diagonal right here
and if I drew in another diagonal,
there is only two diagonals in a parallelogram,
notice these are not
going to be congruent to each other.
But what will happen is that
this point right here will bisect that
diagonal into two congruent pieces
and this point will bisect the other
diagonal. So I will use --
one, two, three -- four markings to
show that this is bisected.
So you are going to apply this knowledge
in proofs, in problems and in true
and false and fill in
the blank questions.
Unit
Polygons