Is a parallelogram always formed by opposite sides that are both parallel and congruent? Reason your answer.
Yes, a parallelogram is always formed by opposite sides that are both parallel and congruent.
To reason this answer, we can refer to the definition of a parallelogram. A parallelogram is a quadrilateral (a four-sided polygon) with opposite sides that are parallel. This means that the two pairs of opposite sides of a parallelogram never intersect.
In addition to being parallel, opposite sides of a parallelogram are also congruent. This means that they have equal lengths.
To visualize this, let's consider the construction of a parallelogram. Start with a line segment, and draw two parallel lines to the segment at each of its endpoints. Then, connect the corresponding endpoints of the parallel lines. The resulting shape is a parallelogram.
As you can see, the opposite sides of the parallelogram are parallel because they were constructed as parallel lines. Furthermore, since the construction was made using a line segment, the opposite sides are congruent by construction.
Therefore, based on the definition and construction of a parallelogram, we can conclude that a parallelogram is always formed by opposite sides that are both parallel and congruent.
Yes, a parallelogram is always formed by opposite sides that are both parallel and congruent. This can be reasoned out using the definition and properties of a parallelogram.
A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel. By definition, parallel lines never intersect each other, so the opposite sides of a parallelogram do not intersect.
Moreover, in a parallelogram, opposite sides are congruent. This property can be proven using the properties of parallel lines. When two lines are parallel, the alternate interior angles formed by a transversal are congruent. In a parallelogram, opposite sides are formed by parallel lines, and therefore the alternate interior angles formed by the transversals (drawn between opposite sides) are congruent. Since the corresponding angles are congruent, it follows that the opposite sides are congruent as well.
Therefore, a parallelogram is always formed by opposite sides that are both parallel and congruent.