Geometry
Notes…6.2 Properties of Parallelograms
Name:_______________________
Part I. Opposite Sides of Parallelograms
Theorem 6-1: Opposite sides of a parallelogram are ____________________
Proof:
1. ABCD is a parallelogram
1. Given
2. AB || _________
2. ________________________
3. BC || _________
3. ________________________
 3 = __________
5.  1 = __________
4.
4. ________________________
5. ________________________
6. AC = AC
6. ________________________
7.  ABC =  CDA
7. ________________________
8. AB = _________
8. _______________________
9. BC = ________
9. ______________________
Example 1:
Find the length of each side.
a)
b)
TI = ____, IL = ____
x=____, QR=_____, PS=______
Part II. Consecutive Angles of Parallelograms
Consecutive Angles are a pair of angles in a polygon that share a side.
 For example, _______ and _______ are consecutive angles,
_______ and ________ are opposite angles.
Consecutive angles of a parallelogram are ________________________________.
For example: mA  mB  ______
Example 2: Find the missing angle measures
a)
b)
m1 =____
c)
m1 =___, m2 =____, m3 =____
m1 =___, m2 =____, m3 =____
Part III. Opposite Angles of a Parallelogram
Theorem 6-2. Opposite angles of a parallelogram are __________________________.
Example 3: Find the designated angles, using the theorems for parallelograms.
a)
b)
m1 =_______, m2 =________, m3 =______
m1 =_______, m2 =_______, m3 =____
c)
d)
y=_______, mE  _____, mG  _____
m1 =___, m2 =____, m3 =____
Part IV. Proving a parallelogram is a rectangle or a square.
A Rectangle is a parallelogram with 4 ____________
angles
A Square is a parallelogram with 4 ____________angles
and __________ sides are congruent
To show you have a square:
 Opposite Sides are __________
 Two adjacent sides are ____________________.
 One angle is ________ degrees.
To show you have a rectangle:
 Opposite Sides are ___________
 One angle is __________ degrees.
Example: Show the vertices R(-2, -3), S(4, 0), T(3, 2), V(-3, -1)
1. Parallel sides: Slope of RS=___________
Slope of TV= ________
Slope of ST=___________ Slope of VR=_________
________ || _______
and ______ || _______,
therefore RSTV is a parallelogram
2. Right angles: Show RS  ST:
(Slope of RS)(Slope of ST) = ______. Therefore
mS  _______
Applying the above Angle Theorems for Parallelograms:
mT  ______, mV  ________, mR  _________
Part V. Diagonals of a Parallelogram
Theorem 6-3. The ________________ of a parallelogram
_____________________ each other.
AO = _____________ and BO = ______________
Example 4:
a)
x = ___________
d)
b)
c)
EG = ______
x = ___________
e) IK = 46
x=___________
f)
x =______________
y =______________
x=________________
g)
a =_____________
b =_____________