As a result, any parallelogram must have two parallel sides. All squares, rhombuses, and rectangles are included. Trapezoids, kites, and triangles are examples of forms that lack parallel sides since they are not categorized as parallelograms.

However, this does not hold for all polygons. For example, a triangle has only three sides so it cannot have two pairs of **parallel sides**. A pentagon has **five sides** so it can have two pairs of parallel sides but a hexagon has six sides so it cannot have two pairs of parallel sides.

In general, an n-gon has 2n edges so it can have n pairs of **parallel edges**. But an (n+1)-gon has 2(n+1) edges so it cannot have (n+1) pairs of parallel edges.

Thus, the only regular polygons that can have two pairs of **parallel edges** are squares, rhombs, and rectangles. All other polygons do not have this property.

Parallelograms A parallelogram has two parallel and equal-length sides. In addition, opposing angles are equal (angles "A" are the same, and angles "B" are the same). Parallelograms include squares, rectangles, and rhombuses. Quadrilaterals are shapes with **four straight sides** and four right angles between them.

Parallelograms have two pairs of corresponding angles: one pair of angles is congruent, or equal in measure; the other pair is complementary, or opposite in measure. The term "parallel" here means that the two lines are equal in length. Thus, a parallelogram is equal in size to **its opposite side lengths**. A square is a special case of a parallelogram with **all sides** of equal length: it is equal in area to its diagonal.

The diagonals of a parallelogram cross at least twice. If they meet more than twice, then the shape is called a polygon. For example, triangles and squares are both quadrilaterals, but not every quadrilateral is a triangle or square.

It may help to think of a parallelogram as two boxes locked together at the corners. They can't move apart from each other because there's nothing pushing them away from each other. Instead, they change position by rotating around **their shared corner**.

Shapes are parallel if their lines are always the same distance apart and never overlap or touch. The parallelogram, rectangle, square, trapezoid, hexagon, and octagon are examples of forms with **parallel sides**. A trapezoid has **two parallel sides**. A rhombus has **four parallel sides**.

Parallel lines will always have **a constant distance** between them. This means that they will never overlap nor touch each other. Parallel lines can be any length as long as they stay away from each other. If they approach too close then they would no longer be considered parallel.

There are two types of parrallel lines: real and apparent.

Real parallel lines exist in nature and they are found on opposite sides of objects where they will always be at the same distance from the object's center of mass. For example, the lines of support for a ladder are real parallels because they are always at the same distance from the ladder's center of mass. Apparent parallels do not exist in nature but they can be drawn by using coordinates in space. For example, if you were to represent every point on or near the surface of the earth with its x and y coordinates, then the line going through these points would be an apparent parallel to the equator.

Apparent parallels can also be created by **visual cues** such as angles or proportions.

Trapezoids are defined by some as having one and only one pair of opposing sides parallel, while others describe trapezoids as having at least one pair of **opposite sides** parallel. (* Rhombuses are quadrilaterals with equal length sides. Quadrilaterals with equal side lengths and four right angles are known as squares. Squares with two pairs of opposite sides parallel are called rhombs. Squares with only one pair of opposite sides parallel are called trapezoids.) Trapezoids are used in engineering projects to create flat surfaces where vertical posts will be attached later.

It is important to understand that any trapezoid can be divided into two similar rectangles, but not all rectangles are trapezoids. A rectangle with one pair of opposite sides parallel is a trapezoid with a parallel opposite side. A trapezoid with opposite sides that are parallel lines is called a rhombus. Rectangles with four right angles are called squares. Squares with two pairs of opposite sides parallel are called rhombs. Trapezoids more than one pair of opposite sides parallel are called polytrapeazoids.

It is also important to understand **that words** like "trap" or "poly" mean many. So a trapizoid is a many-sided figure like a trapezoid, and a polytrapeazoid is a figure with many traps/polygons.

Is it possible for a parallelogram to have **perpendicular sides**? No, not at all. A parallelogram is a four-sided form with opposite sides that are parallel and of equal length. Parallelograms do not always have perpendicular sides. For example, the side lengths of a trapezoid are not perpendicular.

Why does this happen? The reason is that you can rotate any parallelogram around its center point through 90 degrees (or half angles) and get another valid representation of the same figure. For example, consider the following diagram:

Here, the top left corner has been rotated through **90 degrees** about its center point. This forms a new parallelogram with opposite sides of equal length. But since these two sides are now aligned instead of being perpendicular, the statement that "a parallelogram has opposite sides that are parallel and of equal length" has been violated.

It's important to understand that a parallelogram can be transformed into **many other different figures** by simply rotating it through **some number** of degrees.