SWBAT: Prove a Quadrilateral is a Parallelogram
Proving a Quad
is a
Parallelogram
SWBAT: Prove a Quadrilateral is a Parallelogram
Warm – Up
SWBAT: Prove a Quadrilateral is a Parallelogram
If quad has opp. sides || 
(by definition)
If quad has opp. sides  
If quad has opp. angles  
If quad has diags. bisecting each other 
If quad has an  suppl. to cons. s 
6. If quad has a pair of opposite sides  and || 
SWBAT: Prove a Quadrilateral is a Parallelogram
Determining if a quadrilateral is a parallelogram
Analyzing a Diagram
a.
b.
SWBAT: Prove a Quadrilateral is a Parallelogram
Determining if a quadrilateral is a parallelogram
Analyzing a Diagram
c.
d.
SWBAT: Prove a Quadrilateral is a Parallelogram
Determining if a quadrilateral is a parallelogram
Analyzing a Diagram
e.
SWBAT: Prove a Quadrilateral is a Parallelogram
No; opp sides not 
No!
Yes; opp sides ll
Yes; a pair of opp sides 
and ll
Yes; a pair of opp sides Yes; diags bisect each
other
and ll
Yes; opp sides 
Yes; opp s 
SWBAT: Prove a Quadrilateral is a Parallelogram
SWBAT: Prove a Quadrilateral is a Parallelogram
SWBAT: Prove a Quadrilateral is a Parallelogram
SWBAT: Prove a Quadrilateral is a Parallelogram
SWBAT: Prove a Quadrilateral is a Parallelogram
SWBAT: Prove a Quadrilateral is a Parallelogram
1. ACDF is a
2. FD  CA, AF  DC
3. FD  CA, AF  DC
4. A  D
5. AFB  ECD
6. ∆AFB  ∆DCE
7. AB  DE
8. FE  CB
9. FBCE is a
1. Given
2. Def of a
3.
4.
5. Given
6. ASA (4, 3, 5)
7. CPCTC
8. Subtraction Post (3, 7)
9.
(8, 2)
SWBAT: Prove a Quadrilateral is a Parallelogram
6 ways to prove that a quadrilateral
is a parallelogram.
SWBAT: Prove a Quadrilateral is a Parallelogram
6 ways to prove that a quadrilateral
is a parallelogram.