A parallelogram is a special quadrilateral with both pairs of opposite sides parallel as shown in the figure below. Notice that the opposite sides that are parallel lines are shown using the same amount of arrow heads.
Squares, rectangles, and rhombuses are also parallelograms, more specifically special parallelograms, since their opposite sides are parallel according to the definition.
A rhombus is a parallelogram with four equal sides.
A rectangle is a parallelogram with four right angles
A square is a parallelogram with four equal sides and four right angles. Therefore, a square is a rhombus and a rectangle at the same time.
The diagonal of a parallelogram is a line segment that joins two vertices that are not next to each other. A parallelogram has two diagonals. The diagonals are shown in black in the figure below.
A base of a parallelogram is any of its sides.
The altitude of a parallelogram is a line segment that starts from a vertex and is either perpendicular to the base or to the line containing the base.
In the figure above, the altitude is perpendicular to the base. However, in the figure below, the altitude is perpendicular to the line containing the base.
The height of a parallelogram is the length of an altitude.
Please check the lesson about properties of a parallelogram to learn more about these 5 properties of parallelograms.
You can easily construct a parallelogram by following carefully the following 4 straightforward steps.
Step 1
Draw an angle ABC of any measure
Step 2
Put the needle of a compass at point B and adjust the opening of the compass to measure the length of segment BA. Then, keeping the opening of the compass the same, put the needle of the compass at point C and draw an arc.
Step 3
Put the needle of a compass at point B and adjust the opening of the compass to measure the length of segment BC. Then, keeping the opening of the compass the same, put the needle of the compass at point A and draw an arc.
Step 4
Label the point of intersection of the two arcs D. Then, draw line segments AD and CD.
Suppose you have a parallelogram ABCD. The perimeter is equal to the sum of the lengths of its sides.
The length of segment AB is equal to the length of segment CD.
The length of segment BC is equal to the length of segment AD.
Perimeter = length of segment AB + length of segment AB + length of segment BC + length of segment BC
Perimeter = 2(length of segment AB) + 2(length of segment BC)
The area of a parallelogram is the product of the base and the length of the altitude.
Let h be the length of the altitude or the height of the parallelogram.
Then, the formula to use to find the area of a parallelogram is area = b × h
Notice that the term base refers both to the length of the base and the segment.