1. 6.3 Proving Quadrilaterals are ||’ograms
Pg 338

2. Thm 6.6 A B __ ABCD is a parallelogram __ __ C D __
If both pairs of opposite sides of a quadrilateral then the quadrilateral is a parallelogram. A B __
ABCD is a parallelogram __ __ C D __

3. Thm 6.7 B A (( ) ABCD is a parallelogram )) ( D C
If both pair of opposite s of a quadrilateral then the quadrilateral is a ||’ogram. B A (( )
ABCD is a parallelogram )) ( D C

4. Thm 6.8 B A (180-x) x ABCD is a parallelogram x C D
If an  of a quadrilateral is supplementary to both of its consecutive s, then the quadrilateral is a ||’ogram. B A
(180-x) x
ABCD is a parallelogram x C D

5. Thm 6.9 B A __ __ __ __ D C ABCD is a parallelogram
If the diagonals of a quadrilateral bisects each other, then the quadrilateral is a ||’ogram. B A __ __ __ __ D C
ABCD is a parallelogram

6. Thm 6.10 B A > ABCD is a parallelogram > C D
If one pair of opposite sides of a quadrilateral are  and || then the quadrilateral is a ||’ogram. B A
>
ABCD is a parallelogram
> C D

7. Example determine whether the a quadrilateral is a ||’ogram and explain why or why not.__
Yes it’s a ||’ogram because both pair of opposite sides __ __ __

8. Example cont. B A __ ) __ ( __ D C
Yes because the 2 triangles are  by SAS post, so it’s a parallelogram because both pairs of sides are . B A __ ) __ __ ( D C

9. Example cont. > ^ ^ >
Yes because its parallelogram by the def of a parallelogram.
> ^ ^
>

10. Example cont.
No, because consecutive ‘s are not supplementary.
65o
65o
110o

11. Example Prove that the pts. represent the vertices of a ||’ogram
J (-6,2)
K(-1,3)
L(2,-3)
M(-3,-4)
Graph; then use one of today’s theorems and distance formula and/or slope formula or use def of a parallelogram and slope formula.

12. Example cont. Using thm 6.6 and distance formula
JK=
ML=

13. Example using distance formula cont.
JM=
Both pairs of opp sides
KL=

14. Example cont using the def of ||’ogram and slope
m of JK=
m of ML=

15. Example cont.
m of JM=
Opposite side are ll
m of KL=

16. Assignment