6.2 P ROPERTIES OF P ARALLELOGRAMS OBJECTIVES: Prove and apply properties of parallelograms. Use properties of parallelograms to solve problems.

6.2 P ROPERTIES OF P ARALLELOGRAMS Parallelogram ABCD: ( ABCD): 1.Opposite sides are parallel. 2.Opposite sides are congruent. 3.Opposite angles are congruent. 4.Consecutive angles are supplementary 5.The diagonals bisect each other. A D C B

6.2 P ROPERTIES OF P ARALLELOGRAMS D C F E G Example 1: In CDEF, DE = 74 mm, DG = 31 mm and m  FCD = 42 . Find: a)CF b)DF c)m  EFC

6.2 P ROPERTIES OF P ARALLELOGRAMS Example 2: WXYZ is a parallelogram. Find a and b. W Z Y X

6.2 P ROPERTIES OF P ARALLELOGRAMS F E H G J 4z  9 2z w + 8 3w Example 3: EFGH is a parallelogram. Find w and z.

6.2 P ROPERTIES OF P ARALLELOGRAMS Example 3: Three vertices of JKLM are J(3,-8), K(-2,2) and L(2,6). Find the coordinates of vertex M. Step 1: Graph the given points J K L Step 2: Find the slope of Step 3: Start at J and count Up 4, to the right 4. Up 4, to the right 4 Step 4: Plot M and draw sides.  M