Review for Parallelogram
Properties Quiz
G.GPE.B.4 Use coordinates to prove simple
geometric theorems algebraically. For example,
prove or disprove that a figure defined by four given
points in the coordinate plane is a rectangle.
Warm-up
 Show
that A(2, -1), B(1, 3), C(6, 5),
and D(7, 1) are the vertices of a
parallelogram.
Method 1
Show that opposite sides have the same slope, so they are
parallel.
Slope of
AB 
Slope of
CD 
Slope of
BC 
Slope of
DA 
3  ( 1)
12
15
76
53
6 1
 4

1  1
27
 4
2
5

2
5
AB and CD have the same slope so they are parallel.

Similarly,
BC
DA . Because opposite sides are parallel,
ABCD is a parallelogram.
Method 2

Show that opposite sides have the same length.
AB 
(1  2 )  3  (  1)  
CD 
( 7  6 )  (1  5 ) 
17
BC 
( 6  1)  ( 5  3) 
29
DA 
( 2  7 )  (  1  1) 
2
2
2
2
2
2
2
2
17
29
AB  CD and BC  DA . Because both pairs of opposite

sides are congruent,
ABCD is a parallelogram.
Method 3
Show that one pair of opposite sides is congruent and parallel.
Find the slopes and lengths of
Slope of
AB  Slope of
AB  CD 
AB and CD as shown in Methods 1 and 2.
CD  4
17
AB and CD are congruent and parallel,
so ABCD is a parallelogram.
Sometimes, Always or
Never True

The diagonals of a parallelogram are congruent.
Sometimes,
if it’s a
rectangle.
 The consecutive angles of a rectangle are congruent
and supplementary.
Always
 The diagonals of a rectangle bisect each other.
Always
 The diagonals of a rectangle bisect the angles.
Sometimes, if it’s
a square.
 The diagonals of a square are perpendicular
bisectors of eachAlways
other.
 A square is a rectangle.
Always
Sometimes, Always or
Never True
 A diagonal divides a square into two isosceles right
triangles.
Always
 Consecutive angles in a parallelogram are congruent
Sometimes, if it’s a square or a rectangle. Consecutive angles
are always supplementary.
B(1, 5) O(9, 9) X(11, 5) Y(3, 1)
 Is
BOXY a rectangle? Why?
 The
diagonals of BOXY are
__________________

More Practice!!!
1.
D
C
2.
D
C
2x - 7
A
x+9
B
Perimeter ABCD = 46
Find the measure of
16
7
AB __________,
BC _______________.
4x +3
A
63
B
Perimeter ABCD = 16x – 12.
75
Measure of AD =_____________
READY FOR A
CHALLENGE???
Find the coordinates of point M in parallelogram PRAM
(b-a, c)
M(?, ?)
P
A(b, c)
R(a, 0)