1. Advanced Geometry Polygons Lesson 2
Parallelograms

2. Parallelogram
both pairs of opposite sides are parallel

3. Characteristics of Parallelograms
Opposite sides are congruent.
Opposite angles are congruent.

4. Characteristics of Parallelograms (cont.)
Consecutive angles are supplementary.

5. Characteristics of Parallelograms (cont.)
The diagonals of a parallelogram
bisect each other.

6. Characteristics of Parallelograms (cont.)
Each diagonal separates the parallelogram
into two congruent triangles.

7. Example:
Quadrilateral RSTU is a parallelogram. Find RS, y,
m∠UTR, m∠STU, and m∠RST.

8. Example:
Parallelogram JKLM has diagonals and
that intersect at N. If JN = 6x – 4, JL = 8x,
NM = x + 3y, and KN = 2y + 7, find x, y, and KM.

9. Example:
Use the definition of parallelogram to verify
that quadrilateral LMNP is a parallelogram.

10. Characteristics Parallelogram Def.: opp. sides parallel opp. sides 
opp. angles 
consec. angles supp.
diagonals bisect each other
each diagonal creates  triangles