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Classifying
Quadrilaterals
Properties of
Parallelograms
Rectangles
Rhombii
Trapezoids and
Kites
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Classify the following diagram
in as many ways as possible.
Quadrilateral
Parallelogram
Rhombus
Name the quadrilateral that
has two pairs of adjacent
sides that are congruent and
no opposite sides congruent.
Kite
What is the difference
between a trapezoid and
an isosceles trapezoid?
A trapezoid is a quadrilateral with
exactly one pair of parallel sides.
An isosceles trapezoid is a
trapezoid whose nonparallel
opposite sides are congruent.
Find the value of x and y and then
find the length of each side of the
rhombus below.
x=3
y=5
All sides lengths are 15
Complete the following diagram
representing the relationships
among special quadrilaterals.
Opposite sides of a parallelogram
are _________________
Congruent
Explain why consecutive
angles in a parallelogram are
supplementary.
Consecutive angles are formed by two parallel
lines cut by a transversal. These angle pairs are
classified as same-side interior angles and sameside interior angles are supplementary when two
parallel lines are cut by a transversal.
Based on the markings, decide
whether each figure must be a
parallelogram.
a.
b.
a. Yes; both pairs of alternate interior
angles are congruent, therefore both
pairs of opposite sides are parallel.
b. No; the diagonals do not necessarily
bisect each other.
Find the values of x and y for
the parallelogram below.
x = 30
y = 55
Find the values of x and y and then
find the length of each diagonal for
the parallelogram below.
x=8
y = 25
50; 80
Fill in the blank with always,
sometimes, or never.
A rectangle is
___________ a square.
Sometimes
What is the relationship between
the diagonals of a rectangle?
They are congruent
True or False?
a. The opposite sides of a rectangle are congruent.
b. The diagonals of a rectangle are always
perpendicular.
c. The diagonals of a rectangle bisect each other.
d. The opposite angles of a rectangle are both
congruent and supplementary.
a. True; a rectangle is a parallelogram and the
opposite sides of a parallelogram are congruent
b. False; unless the rectangle is a square, the
diagonals are not perpendicular.
c. True; a rectangle is a parallelogram and the
diagonals of a parallelogram bisect each other.
d. True; all four angles in a rectangle are 90
degrees, therefore the opposite angles are both
congruent and supplementary.
Determine if the following diagrams
are rectangles. Justify your answer.
a.
b.
a. No; the diagonals are not
necessarily congruent.
b. Yes; the diagonals are
congruent.
Find the value of x for the
following rectangle and then find
the length of each diagonal.
RZ  x  3
SW  x  5
x = 11
AC = BD = 16
What are the characteristics
of a rhombus?
A rhombus is a
parallelogram with all four
sides congruent.
True or False?
A square is a rhombus.
True
Based on the following
diagram, determine if the
parallelogram is a rhombus.
Yes; the diagonal is
bisecting two angles.
Find the missing angle measures
for the rhombus below.
90; 60; 60; 30
Find the value of x for
which ABCD is a rhombus.
x = 4/3
y=7
Find the value of x for the
isosceles trapezoid below.
x=3
Find the measure of each angle
for the isosceles trapezoid below.
Justify your answer.
1 = 62; base angles of an isosceles
trapezoid are congruent.
2 = 118; angle 2 and the 62 degree
angle are s.s.-interior angles.
3 = 118; angles 2 and 3 are base
angles.
Find the value of x for the
isosceles trapezoid below.
x=4
Find the value of each missing
angle for the kite below.
90; 9; 81; 40
Find the values of x and y
for the kite below.
x = 35
y = 30