Download Geometry Notes G.9 Parallelograms Mrs. Grieser Name: Date: Blo

Geometry Notes G.9 Parallelograms
Mrs. Grieser
Name: ____________________________________________ Date: _______________ Block: _______
Parallelograms

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Parallelograms have:
o 2 sets of parallel sides
o 2 sets of congruent sides
o opposite angles congruent
o consecutive angles supplementary
o diagonals bisect each other
o diagonals form two congruent triangles
Theorems:
 A quadrilateral is a parallelogram IFF both pairs of its opposite sides are congruent.

A quadrilateral is a parallelogram IFF both pairs of its opposite angles are congruent.
Examples:
a) Find x and y.
b) Explain how you know
quadrilateral QRST is a
parallelogram:
Theorem:
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
Example: Find x.
Theorem:
A quadrilateral is a parallelogram IFF the diagonals bisect each other.
a)
Find a and b.
b) For what value of x is
□CDEF a parallelogram?
Theorem:
If one pair of opposite sides of a quadrilateral is congruent and parallel,
then the quadrilateral is a parallelogram.
Example: For what value of x is □FGHJ a parallelogram?
Geometry Notes G.9 Parallelograms
Summary:
sides
angles
Mrs. Grieser Page 2
If we KNOW it’s a parallelogram, then: If we want to PROVE it’s a parallelogram:
Opposite sides are parallel
Show both sides parallel
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are
supplementary
Diagonals bisect each other
Diagonals Diagonals form two congruent
triangles
Combo
Show both sides congruent
Show both angles congruent
Show an angle supplementary to BOTH
consecutive angles
Show diagonals bisect each other
Show one pair of opposite sides
congruent and parallel
You try…
a) Find x and y
d) Find NM, KM, mJML , and
mKML
g) For what value of x is the
figure a parallelogram?
b) Find p and the measures of
the remaining two angles
c) Find x and y and mJ and
e) For what value of x is the
figure a parallelogram?
f)
For what value of x is the
figure a parallelogram?
h) Three vertices of □ABCD are
given. Find the coordinates
of D.
i)
Show that the figure is a
A(-2, -3), B(4, -3), C(3, 2),
D(x, y)
mG
parallelogram: