Chapter 6.3
1.
2.
3.
If opposite sides of a quadrilateral are
//, then it is a //ogram. (definition)
If both pairs of opposite sides of a
quadrilateral are , then it is a
//ogram.
If both pairs of opposite angles are ,
then it is a //ogram.
4.
5.
6.
If an angle of a quadrilateral is supplementary
to both of its consecutive angles, then it is a
//ogram.
If the diagonals bisect each other, then it is a
parallelogram.
If one pair of opposite sides of a
quadrilateral are // and , then it is a
parallelogram.
(new)
Additional
Test for a //ogram
Yes. Opposite Angles are Congruent.
No, not enough information.
Yes. Opposite Sides are Parallel (definition).
Yes. One pair of opposite sides are parallel
and congruent.
120o
60o
120o
Yes. An angle is supplementary to both of its
consecutive angles.
No, not enough information.
Yes. Opposite Sides are Congruent.
120o
60o
No, not enough information.
Yes. Diagonals bisect each other.
No, not enough information.
A
B
ABC  CDA
D
C
Yes, Opposite sides are congruent.
Others can be proven as well.

Distance Formula
d  ( x2  x1 )  ( y2  y1 )
2
• Midpoint Formula
2
 x1  x2 y1  y2 
( xm , y m )  
,

2 
 2
• Slope// lines have equal slope
y2  y1
slope 
x2  x1
Slope Method
Distance Method Slope & Distance
 Prove AB//CD  Prove AB = CD • Prove AB = CD
and AB // CD
and BC//AD
and BC = AD
• Use Distance
 Use slope
 Use Distance
Formula to show
formula and
Formula to
that their lengths
show that their
show that their
are equal and
slopes are equal.
lengths are
use slope
equal.
Midpoint Method
• Prove the diagonals bisect each other
• Show that the diagonals have the
same midpoint.
formula to show
that their slopes
are equal.
Proof:
Since ΔXVY  ΔZVW and ΔXVW  ΔZVY,
by CPCTC. By which
method would you prove WXYZ is a parallelogram?
A. Both pairs of opp. sides .
B. Both pairs of opp. ’s .
C. One pair of opp. sides both 
and ||.
D. Diagonals bisect each other
Properties of Parallelograms
Determine whether the quadrilateral is a parallelogram.
Justify your answer.
Answer: Each pair of opposite sides has the same
measure. Therefore, they are congruent. If both
pairs of opposite sides of a quadrilateral are
congruent, the quadrilateral is a parallelogram.
Which method would prove the
quadrilateral is a parallelogram?
A. Both pairs of opp.
sides ||.
B. Both pairs of opp.
sides .
C. Both pairs of opp.
’s .
D. One pair of opp.
sides both || and .
Find x so that the quadrilateral is a //ogram.
Opposite sides of a
//ogram are congruent.
Find m so that the quadrilateral is a //ogram.
A. m = 2
B. m = 3
C. m = 6
D. m = 8
Use Slope and Distance
COORDINATE GEOMETRY Determine whether the
figure with vertices A(–3, 0), B(–1, 3), C(3, 2), and
D(1, –1) is a parallelogram. Use the Slope Formula.
3
slope of AB 
2
1
slope of AD  
4
= slopes  // Lines
1
slope of BC  
4
3
slope of CD 
2
Opp. Sides are //  //ogram
Determine whether the figure with the given vertices is a
parallelogram. Use the method indicated.
A(–1, –2), B(–3, 1), C(1, 2), D(3, –1); Slope Formula
A. yes
B. no
C. cannot be
determined
1.
2.
3.
A
B
C
Chapter 6.3
 Pg 337:
3-14, 20-25, 26, 28,
45-48