GEOMETRY: PARALLELOGRAMS
COMMON MISTAKES
1
10/20/2009
Geometry-Parallelograms
Defining Parallelograms
and the Quadrilaterals
They Include
Definition-PARALLELOGRAMS are
quadrilaterals (4 sided polygons)
whose opposite sides are congruent
and parallel; and whose opposite
angles are also congruent. The
diagonals of a parallelogram bisect
(divide a segment into two congruent
segments) each other.
RECTANGLES-are parallelograms
with 4 right angles.
SQUARES-parallelograms with 4
right angles and 4 congruent sides.
A square is a special type of
Rectangle and Rhombus.
RHOMBUSES-are parallelograms
whose diagonals are perpendicular.




2
Common Mistakes
Forgetting which properties belong to
which quadrilateral.
L
M
W
X

P


N Z
Y
Incorrect: Parallelogram WXYZ has
4 right angles.
Correct: Rectangle LMNP has
4 right angles.
Parallelogram WXYZ has
opposite angles congruent.
10/20/2009
Geometry-Parallelograms and Perimeter
How to Understand the
Perimeter Concept.

Perimeter of Polygons is the term
used to describe the linear
measurement around a polygon.

Units of Perimeter are the same as
those given for length (i.e. cm, ft, yd, m,
etc.)
Common Mistakes
Confusing Perimeter with Area
(the amount “inside” a polygon);
even using the wrong units.
J
K

10 in
M
Perimeter Formulas:

Pparalle log ram = 2 • length + 2 • width Incorrect: =
P
Prec tan gle = 2 • length + 2 • width
Psquare= 4 • side
Pr hom bus= 4 • side
3
L
13 in
13in • 10in
= 130in2
Correct:
Prec tan gle = 2 • 13in + 2 • 10in
Prec tan gle = 46in
10/20/2009
Geometry– Parallelograms and Area
Understanding the Concept Common Mistakes
of Area of Parallelograms
Area of a polygon applies to the “stuff”
inside the polygon where as perimeter is
the distance around the polygon.
AREA
AREA-units become 2-Dimensional
(sq cm, sq ft, sq m, etc.)
Area Formulas for Parallelograms:
A paralle log=
base • height
ram


A rec
length • width
=
tan gle
A square = side2
A r hom bus diagonal1 • diagonal2
=
4
ALL Area formulas for parallelograms
deal with two dimensions, called either
the base and height or length and
width. These 2 measurements are
multiplied together; and thus, the units
are “squared”( to the second degree
or 2-Dimensional)
“height” of a parallelogram or
any polygon- refers to the figure’s
perpendicular height not the side
length.
h
Side length
10/20/2009