A parallelogram is quadrilateral comprised of two pairs of parallel lines. There are several rules involving

This Page:
 Angles
 Sides
 Diagonals
 Interactive Parallelogram
Interactive Parallelogram
The full size interactive parallelogram has additional features such as the lengths of the diagonals.
Two Pairs of Parallel Lines
To create a parallelogram just think of 2 different pairs of parallel lines intersecting. ABCD is a parallelogram.
Angles of A Parallelogram
Opposite Angles are Congruent
$$ \angle D \cong \angle B \\ \angle A \cong \angle C $$
Triangles can be used to prove this rule about the opposite angle.
Consecutive angles are supplementary
The following pairs of angles are supplementary
$$ \angle C $$ and $$ \angle D $$
$$ \angle C $$ 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.
$$ \angle A = 80° $$ since opposite angles are congruent.
Since consecutive angles are supplementary
You can then find $$ \angle C $$ easily since it is opposite of $$ \angle B $$
$$ \angle C= 80° $$ one = 25° (this is the opposite angle)
 another = 18025 = 155° (a consecutive angle)
 a third = 18025 = 155°; (a consecutive angle)
Sides of a Parallelogram
The opposite sides of a parallelogram are congruentTriangles 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
Since opposite sides are congruent you can set up the following equations:
2x − 10 = x + 80 and solve for x
3y − 4 = y + 20 and solve for y
y = 12
Diagonals of a Parallelogram
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
Since the diagonals bisect each other, y = 16 and x = 22
x + 40 = 2x + 18
40 = x +18
40 = x + 18
22 = x

Properties of parallelograms:
 Angles
 Sides
 Diagonals
 Interactive Parallelogram
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