define a parallelgram.write it's propety
Answers
Answer:
A parallelogram is a flat shape with four straight, connected sides so that opposite sides are congurent and parallel
Step-by-step explanation:
A parallelogram is a flat shape with four straight, connected sides so that opposite sides are congruent and parallel. This means a parallelogram is a plane figure, a closed shape, and a quadrilateral.
You can have almost all of these qualities and still not have a parallelogram. If the four sides do not connect at their endpoints, you do not have a closed shape; no parallelogram! If one side is longer than its opposite side, you do not have parallel sides; no parallelogram! If only one set of opposite sides are congruent, you do not have a parallelogram, you have a trapezoid
Start at any vertex (corner). Write a capital letter, then move either clockwise or counterclockwise to the next vertex. Use a different capital letter. For our parallelogram, we will label it
W
X
Y
Z
, but you can use any four letters as long as they are not the same as each other.
parallelogram sides angles
The four line segments making up the parallelogram are
W
X
,
X
Y
,
Y
Z
, and
Z
W
. Notice that line segments
W
X
and
Y
Z
are congruent. Line segments
X
Y
and
Z
W
are also congruent.
The interior angles are
∠
W
,
∠
X
,
∠
Y
, and
∠
Z
. The opposite angles are congruent. In our parallelogram, that means
∠
W
=
∠
Y
and
∠
X
=
∠
Z
.
Connecting opposite (non-adjacent) vertices gives you diagonals
W
Y
and
X
Z
. One interesting property of a parallelogram is that its two diagonals bisect each other (cut each other in half). Another property is that each diagonal forms two congruent triangles inside the parallelogram.
Properties of Parallelograms
For such simple shapes, parallelograms have some interesting properties. You can examine them based on their diagonals, their sides or their interior angles. We already mentioned that their diagonals bisect each other. Let's look at their sides and angles.
Parallelogram Sides
Opposite sides are parallel -- Look at the parallelogram in our drawing. The bottom (base) side
Y
Z
and top
W
X
are parallel; if you were to extend their line segments, they would never meet. The left and right sides (
X
Y
and
Z
W
) are also parallel.
Opposite sides are congruent -- The base side (
Y
Z
) and the top side (
W
X
) of our parallelogram are equal in length (congruent); the left side (
X
Y
) and right side (
Z
W
) are also congruent
Parallelogram Properties: Sides
To be a parallelogram, the base and top sides must be parallel and congruent, and so must the left and right sides.
The base and top side make a congruent pair. The left and right side make a congruent pair. The two pairs of congruent sides may be, but do not have to be, congruent to each other.