Download 6-2 Parallelograms 6-4 Rectangles

Advanced Geometry
Polygons
Lesson 2
Parallelograms
Parallelogram
both pairs of opposite sides are parallel
Characteristics of Parallelograms
 Opposite sides are congruent.
AB  DC
AD  BC
 Opposite angles are congruent.
A  C
B  D
Characteristics of Parallelograms (cont.)
 Consecutive angles are supplementary.
mA  mB  180
mB  mC  180
mC  mD  180
mD  mA  180
Characteristics of Parallelograms (cont.)
 The diagonals of a parallelogram
bisect each other.
AE  EC
BE  ED
Characteristics of Parallelograms (cont.)
 Each diagonal separates the parallelogram
into two congruent triangles.
ABC  CDA
ABD  CDB
Example:
Quadrilateral RSTU is a parallelogram. Find RS, y,
m∠UTR, m∠STU, and m∠RST.
Example:
Parallelogram JKLM has diagonals KM and JL
that intersect at N. If JN = 6x – 4, JL = 8x,
NM = x + 3y, and KN = 2y + 7, find x, y, and KM.
Example:
Use the definition of parallelogram to verify
that quadrilateral LMNP is a parallelogram.
Characteristics
Parallelogram
• Def.: opp. sides parallel
• opp. sides 
• opp. angles 
• consec. angles supp.
• diagonals bisect each other
• each diagonal creates  triangles