Ch. 6: Parallelograms,
Rhombus, and Rectangles
Possible or Impossible for the
described quadrilateral
to be a parallelogram…
Question 1: Possible/Impossible?
• A diagonal of a parallelogram bisects two
angles of the parallelogram. Is it possible
for the parallelogram to have sides of
lengths 5, 6, 5, and 6?
Impossible
• If one diagonal bisects two angles, then
the figures is a rhombus. A rhombus has 4
congruent sides.
Question 2: Possible/Impossible
• Each diagonal is 15 cm long and one
angle of the quadrilateral has measure 45.
Impossible
• If diagonals or a parallelogram are
congruent, the quadrilateral is a rectangle,
but a rectangle has four right angles
Question 3: Possible/Impossible
• The diagonals are congruent,
perpendicular and bisect each other.
Possible
• If diagonals of a parallelogram are
congruent, the quadrilateral is a rectangle.
It the diagonals of a parallelogram are
perpendicular, the quadrilateral is a
rhombus, and a rectangle that is a
rhombus is a square.
Question 4: Possible/Impossible
• Each diagonal of a parallelogram is 3 cm
long and two opposite sides are 2 cm long
Possible
• Yes, congruent diagonals in a
parallelogram mean that the figure is a
rectangle with two opposite sides 2 cm.
long.
Question 5: Possible/Impossible
• A diagonal of a parallelogram bisects an
angle and has side lengths of 4 and 2.
Impossible
• If a figure is a parallelogram then the angle
opposite the bisected angle is also
bisected so the figure is a rhombus. A
rhombus has 4 congruent sides.
Question 6: Possible/Impossible
• A parallelogram has a 90 degree angle
and diagonals that are perpendicular to
each other?
Possible
• Perpendicular diagonals and right angle
could be a square
Question 7: Possible/ Impossible
• The parallelogram has congruent
diagonals and one angle of 60 degrees.
Impossible
• A parallelogram with congruent diagonals
is a rectangle with four right angles.
Question 8: Possible/Impossible
• The parallelogram has perpendicular
diagonals and four right angles.
Possible
• Perpendicular diagonals means the figure
is a rhombus. Four 90 degree angles
means that it is a rectangle. Both
properties imply it is a square.