Warm-Up 1) Draw a convex quadrilateral 2) Draw a concave quadrilateral 3) Draw a regular hexagon 4) Draw a concave pentagon

Geometry 6-2 Properties of Parallelograms

Definition A quadrilateral with two pairs of parallel sides is a parallelogram. To write the name of a parallelogram, you use the symbol

Properties of Parallelograms If a quadrilateral is a parallelogram, then… –The opposite sides are congruent –The opposite angles are congruent –The consecutive angles are supplementary –The diagonals bisect each other

BC = ADBZ = DZ AB = DCAZ = CZ  B   DBC || AD  A   CAB || DC  A +  B = 180  B +  C = 180

Example In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. CF = GF = mDEF = mCDE =

Example Find the length of… WX = mWXY =

Example Find the length of… FH = EG =

Find the Missing Point Three vertices of JKLM are J(3, –8), K(–2, 2), and L(2, 6). Find the coordinates of vertex M. J K L Since JKLM is a parallelogram, both pairs of opposite sides must be parallel.