Download Given: ABCD is a parallelogram

Geometry B – Notes Section 6.3
Definitions and Theorems involving parallelograms
1.
2.
3.
4.
5.
Given: ABCD is a parallelogram
Statements
Reasons
Prove: AGB  CGD
D
C
1
3
5
6
2
G
4
A
B
Determine which of the figures below are parallelograms. If so, which definition or theorem proves it is a
parallelogram.
D
60
C
D
C
120
A
B
A
D
C
B
D
60
120
A
B
60
A
B
C
AD  BC, 1  2
AB // DC, E is the midpoint of AE
A
A
B
B
1
E
E
2
C
D
D
C
Yesterday we looked at two ways to prove a figure is a parallelogram while graphing.
What were those two ways and what formulas did you use?
1.
How many times do you use that formula?_____________
2.
How many times do you have to use the formula?______________
A former student said she could prove a figure was a parallelogram by using the midpoint formula only 2
times. Look back at the 5 theorems concerning parallelograms and determine how the midpoint formula
could be used. Use the example below to help you. Prove that ABCD is a parallelogram.
A(2 , 5)
C(3 , -1)
B(5 , 9)
D(6 , 3)
Geometry – Proving a Parallelogram
Definition of a parallelogram – A quadrilateral with opposite sides parallel.
Diagonals bisects each other
Given:
Prove: ABCD is a parallelogram
A
B
C
D
Opposite Sides Congruent
Given:
Prove: ABCD is a parallelogram
A
B
C
D
Consecutive angles supplementary
Given:
Prove: ABCD is a parallelogram
A
B
C
D
One pair of sides parallel and congruent
Given:
Prove: ABCD is a parallelogram
A
B
D
Opposite angles congruent.-
C
D
D
C
D
C
60
C
120
A
B
A
B
A
B
AD  BC, 1  2
AB //A DC, E is the midpoint of AE
B
A
B
1
E
E
2
C
D
D
C
Below you are going to determine if the figure is a parallelogram.
A(2 , 5)
C(3 , -1)
B(5 , 9)
D(6 , 3)
Determine which formulas can be use when proving a quadrilateral is a parallelogram based on the
following definitions or theorems
Opposite Sides Parallel Opposite angles 
Opposite Sides Diagonals bisect each otherOne pair of sides // and -