Download Specail Parallelograms

6-4 SPECIAL PARALLELOGRAMS
M11.C.1 2.9.11.C
Objectives:
1)
To use properties of diagonals of rhombuses
and rectangles
2)
To determine whether a parallelogram is a
rhombus or a rectangle
THEOREMS

Each diagonal of a
rhombus bisects two
angles of the rhombus

The diagonals of a
rhombus are
perpendicular.
EXAMPLE: FINDING ANGLE MEASURES
MNOP is a rhombus.
 Angle N is 120.
 Find the measure of the
numbered angles

EXAMPLE: PAGE 313

Find the measure of the numbered angles.
THEOREM

The diagonals of a rectangle are congruent.
EXAMPLE: FINDING DIAGONAL LENGTH
Rectangle ABCD
BD = 2y + 4
AC = 6y - 5
THEOREMS
If one diagonal of a parallelogram bisects two
angles of the parallelogram, then the
parallelogram is a rhombus.
 If the diagonals of a parallelogram are
perpendicular, then the parallelogram is a
rhombus.
 If the diagonals of a parallelogram are congruent,
then the parallelogram is a rectangle.

RECOGNIZING SPECIAL PARALLELOGRAMS

1.
2.
3.
Determine whether the quadrilateral can be a
parallelogram. If not, write impossible.
The quadrilateral has congruent diagonals and
one angle of 60 degrees.
The quadrilateral has perpendicular diagonals
and four right angles.
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? Explain.
Homework
 Page 315 #1-21
