Brian McCall

**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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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.