6.3 Showing Quadrilaterals are Parallelograms

Use Consecutive Angles and Diagonals
Tell whether the quadrilateral is a parallelogram. Explain your
reasoning.
4. G 5.
80
H
130
E
60
F
L M
104
76 104
K N
6. R P
7. U V
T
5
4
X
5
4
S
P
T
W
You have learned five ways to show that a quadrilateral is a
parallelogram.
SUMMARY
SHOWING A QUADRILATERAL IS A PARALLELOGRAM
Definition of parallelogram, p. 310
Show that both pairs of opposite sides
are parallel.
Theorem 6.6, p. 316
Show that both pairs of opposite sides
are congruent.
Theorem 6.7, p. 316
Show that both pairs of opposite angles
are congruent.
Theorem 6.8, p. 317
Show that one angle is supplementary
to both of its consecutive angles.
Theorem 6.9, p. 318
Show that the diagonals bisect
each other.
y x
6.3 Showing Quadrilaterals are Parallelograms 319
x
x y 180