G.CO.C.11 STUDENT NOTES WS #2 – geometrycommoncore.com
1
Using the informal method of putting congruent triangles together to form different quadrilaterals we learned
a lot about their characteristics and properties. These properties are critical to solving problems about the
parallelogram family. Let us summarize those properties and discuss how these shapes relate to each other.
PARALLELOGRAM
Definition:
RECTANGLE
Definition:
RHOMBUS
Definition:
SQUARE
Definition:
A quadrilateral with 2
sets of opposite sides
that are parallel.
A parallelogram with 4
congruent angles.
A parallelogram with 4
congruent sides.
A rectangle and a
rhombus.
Notice that the rectangle, rhombus and ultimately the square are define as special types of parallelograms. In
other words all of these quadrilaterals are parallelograms. Because of this they share all of the parallelogram
properties and then have some unique ones from their definition or structure.
PARALLELOGRAM
Properties:
RECTANGLE
Properties:
RHOMBUS
Properties:
SQUARE
Properties:
Opposite Sides are 
Opposite Sides are 
Opposite Sides are 
Opposite Sides are 
Opposite ’s are 
Opposite ’s are 
Opposite ’s are 
Opposite ’s are 
Consecutive ’s are
supplementary
Consecutive ’s are
supplementary
Consecutive ’s are
supplementary
Consecutive ’s are
supplementary
Diagonals bisect
each other
Diagonals bisect
each other
Diagonals bisect
each other
Diagonals bisect
each other
4 Right Angles (Def.)
4 Right Angles
 Diagonals
 Diagonals
4  Sides (Def.)
4  Sides
 Diagonals
 Diagonals
Diagonals bisect ’s
Diagonals bisect ’s
The square is the regular quadrilateral which means that it has 4 equal sides, 4 equal angles and has 4 lines of
symmetry. Notice that it has all of the properties from the parallelogram, rectangle and rhombus making it
the most restricted (specific) parallelogram.
Knowing the characteristics of each type of parallelogram is critical to solving problems in this objective.
G.CO.C.11 STUDENT NOTES WS #2 – geometrycommoncore.com
2
Let’s apply some of these properties to solve problems.
Determine the missing information.
a) Parallelogram ABCD
b) Rhombus ABCD
c) Square ABCD
C
C
x
B
3.2 cm
B
y
E
13°
x
B
12 cm
y
68°
D
C
y
E
x
A
D
A
x = 13 because alternate angles are
equal when lines are parallel.
x = 12 cm because in a rhombus
all four sides are .
D
15 cm
A
x = 15 because all 4 sides are .
y = 90 because diagonals are .
y = 3.2 cm because in a parallelogram
diagonals bisect each other.
d) Rectangle ABCD
e) Rhombus ABCD
12 cm
B
71°
y = 68 because diagonals bisect
angles.
x
f) Parallelogram ABCD
B
5 cm
x
x
D
AC = y
C
62°
C
E
A
B
AC = 12 cm
mBCD = 68°
C
36°
A
E
y
D
E
y
A
x = 19 because mABC = 90.
y = 13 cm because ABC is a right  with
a hypotenuse of AC so 52 + 122 = 132
(Pythagorean Theorem)
D
y = 34 because the diagonals
bisect the angles and alt.
interior ’s are  with parallel
lines.
x = 6 cm because diagonals
bisect each other.
x = 36 because alternate
interior ’s are  with parallel
lines.
y = 82 because the angles of a 
sum to 180.