6-2 Properties of Parallelograms Geometry

Parallelogram B A >> Seg AB ll seg DC And Seg AD ll seg BC < Parallelogram- a quadrilateral with both pairs of opposite side parallel. B A >> Seg AB ll seg DC And Seg AD ll seg BC < < C >> D

Naming a Parallelogram ABCD

Thm 6-2-1 seg PQ @ seg RS and seg SP @ seg QR Q < >> R P If a quadrilateral is a ||’ogram, then its opposite sides are @ . seg PQ @ seg RS and seg SP @ seg QR Q < >> R P >> < S

Ex. 1 ABCD is a parallelogram. AB=14cm. What is CD=?

Thm 6-2-2 If a quad is a ||’ogram then its opposite s are . Q ) P @ R and Q @ S )) R (( P ( S

Ex. 2 JEPT is a ||’ogram. mT =80o, find J, E, & P. mJ= 100 mE=80 mP=100 P

Thm 6-2-3 If a quad is a ||’ogram, then the consecutive angles are supplementary. A B C D

Ex. 3 WXYZ is a parallelogram. Find each measure. a.) YZ b.)m Addl Ex. 2

Thm 6-2-4 If a quad is a ||’ogram then its diagonals bisect each other. Q P M R S

Ex. 4 ||’ogram QRST has diagonals seg QS and seg RT intersecting at W Ex.4 ||’ogram QRST has diagonals seg QS and seg RT intersecting at W. Find WT and WS. Q 15 5 W R T 12 WT=12 WS=5 S

Ex. 5 In CDEF, DE=74 mm, DG = 31 mm, & m FCD = 42 . Find … a.) CF b.) m EFC c.) DF Addl Ex. 1

Ex. 6 Three vertices of JKLM are J(3,-8), K(-2,2) and L(2,6). Find the coordinates of vertex M.

Assignment