1. Properties of Parallelograms

2. Any shape with straight edges that is closed
Polygons
Any shape with straight edges that is closed
Quadrilateral
Any shape with 4 sides

3. Parallelogram

4. Parallelograms are quadrilaterals where both pairs of opposite sides are parallel.
Parallelogram Name: ABDC
AB is opp. CD, thus AB ║ CD
AC is opp. BD, thus AC ║ BD

5. KL  MN KM LN Ex. 1 KLNM is a parallelogram. Find MN and KM.
4 cm
KL  MN
KM LN
8 cm
MN = 4 cm opp. sides are congruent
KM = 8 cm opp. sides are congruent

6. Properties of Angles in Parallelograms

7. mV = 115o opposite ’s are congruent
S T
W V
S = 115°
mV = 115o opposite ’s are congruent
mW = consecutive ’s are supplementary.
mW =
mW = 65o
mT = 65o opposite ’s are congruent

8. Diagonals in Parallelograms
*A diagonal is a line segment that connects the opposite angles

9. NL  JN diagonals bisect
JN= 8cm

10. A quadrilateral is a parallelogram if any of the conditions below are satisfied,
1. Both pairs of opposite sides of a quadrilateral are congruent.
2. Both pairs of opposite angles of a quadrilateral are congruent.
3. An angle of a quadrilateral is supplementary to its consecutive angles.
4. The diagonals of a quadrilateral bisect each other.

11. Tell whether the quadrilateral is a parallelogram or not. Explain.
No, the opposite sides are not congruent.
Yes, both pairs of opposite angles are congruent.
No, the opposite angles are not congruent and the consecutive angles are not all supplementary

12. Yes, one angle is suppl. to both of its consecutive angles.
No, there is not enough information given.
Yes, the diagonals bisect each other.
No, the diagonals do not bisect each other.

13. Area of Parallelograms
A = Base x Height
*base: the parallel sides
*height: the shortest distance between the parallel sides
base
height

14. A = bh
= (13)(5)
= 65 in2