1. 6-3 Conditions for ||’ograms
Geometry

2. Thm 6-3-1 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

3. Thm 6-3-2 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 __

4. Thm 6-3-3 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

5. Thm 6-3-4 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

6. Thm 6-3-5 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

7. Ex. 1a.) Determine whether the quadrilateral is a ||’ogram and explain why or why not.__
Yes it’s a ||’ogram because both pair of opposite sides __ __ __

8. Ex. 1b ) Determine whether the quadrilateral is a ||’ogram and explain why or why not.
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. Ex. 1c) Determine whether the quadrilateral is a ||’ogram and explain why or why not.
Yes because its parallelogram by the def of a parallelogram.
> ^ ^
>

10. Ex. 1d) Determine whether the quadrilateral is a ||’ogram and explain why or why not.
No, because consecutive ‘s are not supplementary.
65o
65o
110o

11. Ex. 2a Show that JKLM is a parallelogram for a=3 & b=9. K 5b+ 6 L
15a a+4
J 8b-21 M

12. Ex. 2b.)
Show that PQRS is a parallelogram for x=10 & y= R
Q S P

13. Ex. 3 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.

14. Ex. 3a.) Using thm 6-3-2 and distance formula
JK=
ML=

15. Ex. 3a.) using distance formula
JM=
KL=
Both pairs of opp sides

16. Ex. 3b.) using the def of ||’ogram and slope
m of JK=
m of ML=

17. Ex. 3b.)
m of JM=
m of KL=
Both pairs of Opposite sides are ll

18. Ex. 3c.) Using thm 6-3-1 one pr. Of opp. Sides are congruent…
JK=
ML=

19. Ex. 3c.) Using Thm. 6-3-1… & parallel
m of JK=
m of ML=
1 pr of opp. Sides are congruent & parallel

20. Assignment