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Definition: Parallelogram is a quadrilateral in which opposite sides are parallel.

Interactivity 1 - Play with a Parallelogram    Упатсво за интерактивноста

Click and drag the slider buttons to change the size. Click and drag point B to move and point А to rotate.

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Basic formulas for a parallelogram with sides a and b and height h: perimeter is: L=2(a+b) , and area is: A=ah .

Examples for perimeter and area of parallelograms

Check the following examples using the above interactivity.

Notice that the length of "side" b does not affect the area and the height h does not affect the perimeter.
a h b Perimeter: L=2(a+b) Area: A=ah
7 \,cm 3 \,cm 4 \,cm 2(7 \,cm+4 \,cm)= 22\,cm 7 \, cm \cdot 3 \,cm=21 \,cm^2
2,5 \, m 4 \,m 7 \,cm 2(2,5 \,m+7 \,m) =19 \,m 2,5 \,m \cdot 4 \,m=10 \,m^2
0,07 \,m 60 \,mm 8 \,cm 2(7 \,cm+8 \,cm) =30 \,cm 7 \,cm \cdot 6 \,cm=42 \,cm^2
0,07 \,m 60 \,mm 8 \,cm 2(0,07 \,m+0,08 \,m) =3,0 \times 10^{-1} \,m 0,07 \,m \cdot 0,06 \,m=4,2 \times 10^{-3} \,m^2

Interactivity 2: Construct a parallelogram

1. Examine the parallelogram in the above interactivity..

2. Now construct a parallelogram with the same properties. If you need help with the steps, click here to open a new window with directions?.

Check whether your construction is stable - Is your construction always a parallelogram no matter what slider or point you move?
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Equivalent definitions:
  1. A quadrilateral is a parallelogram if opposite sides are congruent (same length).
  2. A quadrilateral is a parallelogram if one pair of opposite sides are congruent and parallel.
  3. A quadrilateral is a parallelogram if opposite angles are congruent (same size).
  4. A quadrilateral is a parallelogram if the diagonals bisect each other (cut each other in half).

Theorems

  • A parallelogram is completely determined by the lengths of two adjacent (neighboring) sides and the angle between them.
  • The diagonals of a parallelogram bisect each other.
(This together with 4 above means that a quadrilateral is a parallelogram if and only if the diagonals bisect each other.)

 

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Page last modified on March 07, 2008, at 03:56 PM