6.3Notes: Conditions for Parallelograms
Target: Prove a quadrilateral is a parallelogram in a two column proof.
Target: Show algebraically or in the coordinate plan that a quadrilateral is a parallelogram .
Ways to Prove That a Quadrilateral is a Parallelogram:
1) _______________________________________then the quadrilateral is a parallelogram
2) _______________________________________then the quadrilateral is a parallelogram
3) _______________________________________then the quadrilateral is a parallelogram
4) _______________________________________then the quadrilateral is a parallelogram
5) _______________________________________then the quadrilateral is a parallelogram
6) _______________________________________then the quadrilateral is a parallelogram
Let’s Practice!
1) Show that ABCD is a parallelogram for
x= 7 and y=4
B
2) Show that PQRS is a parallelogram for
a= 2.4 and b=9.
A
R
Q
C
P
D
For #3-6, determine if each quadrilateral must be a parallelogram. Justify your answer.
3)
4)
5)
6)
S
Time for Proofs 
7)
M
A
Given: MA HT
MHA  TAH
H
Prove: MATH is a
T
A
8)
Given: E is the midpoint of BD
B
E
ADE  CBE
Prove: ABCD is a
D
C