Graphing
Calculator
Math
Worksheets
Algebara
Solver
Chart
Maker
A+ A− B

Parallelograms

Properties, Shapes, Diagonals and Area

A parallelogram is quadrilateral comprised of two pairs of parallel lines. There are several rules involving
Interactive Parallelogram
(see full size )
The full size interactive parallelogram has additional features such as the lengths of the diagonals.

Content on this page requires a newer version of Adobe Flash Player.

Get Adobe Flash player

Parallelograms Shape and Properties

Two Pairs of Parallel Lines

To create a paralleogram, just think of 2 different pairs of parallel lines intersecting.
ABCD is a parallelogram.
Parallelograms Shape and Properties Click on the button below to turn the pure parallel lines into a parallelogram.
Make Parallelogram

Angles of A Parallelogram

Opposite Angles are Congruent

Parallelogram Angles Picture
$$ \angle D \cong \angle B \\ \angle A \cong \angle C $$
Triangles can be used to prove this rule about the opposite angle.

Consecutive angles are supplementary.

consecutive angles of a parallelogram The following pairs of angles are supplementary
$$ \angle $$ C and $$ \angle $$ C
$$ \angle $$ C and $$ \angle $$ B
$$ \angle $$ A and $$ \angle $$ B
$$ \angle $$ A and $$ \angle $$ D
To explore these rules governing the angles of a parallelogram use Math Warehouse's interactive parallelogram.


What is the measure of angles A, B and C in parallelogram ABCD?
Answer
b A= 80° since opposite angles are congruent

Since consecutive angles are supplementary.
f

You can then find aC easily since it is opposite of a B
b C= 80°
Picture Angles of Parallelogram  

What is the measure of x, y, z in parallelogram below?
Answer
Paralelogram Angles Diagram
In a parallelogram one of the angles measures 25°, what are the measures of the other angles?
Answer

Sides of a Parallelogram

Sides of Parallelogram


The opposite sides of a parallelogram are congruent.
Triangles can be used to prove this rule about the opposite sides.
. To explore these rules governing the sides of a parallelogram use Math Warehouse's interactive parallelogram
Sides of Parallelogram Diagram What is the length of side BD and side CD in parallelogram ABCD?
Answer
Parallelogram Sides Picture What is x in the parallelogram on the left?
Answer
What is the value of x and y in the parallelogram below?
Answer
Sides of Parallelogram Illlustration

Diagonals of a Parallelogram

Parallelogram Diagonals Bisect Each Other The diagonals of a parallelogram bisect each other
AO = OD
CO = OB
To explore these rules governing the diagonals of a parallelogram use Math Warehouse's interactive parallelogram
What is x and Y?
Answer

Parallelogram Diagonals
What is x?
Answer
Diagonals of Parallelogram DIagram