6.3 Proving Quadrilaterals are ||’ograms Pg 338

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

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

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

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

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

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 are @. __ __ __

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

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

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

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.

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

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

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

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

Assignment