A quadrilateral with **two parallel pairs** of sides. Equivalent circumstances include opposing sides being of **identical length**, opposite angles being equal, and diagonals bisecting each other. The term "opposite quadrilaterals" may also be used.

The four types of opposite quadrilaterals:

Opposite quadrilaterals are those in which two opposite sides are equal. These include squares and rectangles. Opposite quadrilaterals are also called symmetrical quadrilaterals. All quadrilaterals are symmetrical, but not all symmetrical quadrilaterals are quadrilaterals; for example, triangles are symmetrical but not quadrilaterals.

The four factors that must be satisfied for a quadrilateral to be considered equivalent to one of its opposite quadrilaterals:

1 The opposite sides must be equal.

2 The opposite angles must be equal.

3 One diagonal must intersect another at right angles.

4 A vertex must connect to **another vertex** or to both a horizontal and vertical line.

These conditions are sufficient, but not necessary.

- What are the opposite sides of a quadrilateral?
- Does a quadrilateral have rotational symmetry?
- Which quadrilateral has no lines of symmetry and two acute angles?
- What shape is a quadrilateral but is not a parallelogram?
- How do you prove a quadrilateral is congruent?
- What type of quadrilateral has equal diagonals?
- Which is the best way to classify the quadrilateral?

A parallelogram is a quadrilateral having opposing pairs of sides that are parallel. A parallelogram has **180o rotational symmetry** (Order 2). A rectangle is a four-right-angle parallelogram. Rectangles have 180o rotational symmetry (Order 2). A square is a four-right-angle rectangle that is also a parallelogram because its opposite sides are parallel.

Parallelogram: these are the only four polygons with **no lines** of symmetry.

A parallelogram is not a regular quadrilateral with no equal sides. There are no parallel lines on a kite. One set of opposing sides of a trapezium and an isosceles trapezium are parallel. A rhombus has two pairs of parallel sides.

In geometry, a quadrilateral is any figure composed of **four straight lines** or their extensions. A quadrilateral is said to be convex if its opposite angles are less than 180°. If all the opposite angles of a quadrilateral are greater than or equal to 180°, it is called concave. A quadrilateral is called flat if it has **neither angles** that are too large nor angles that are too small. A quadrilateral is called open if one side is longer than the other three; otherwise it is called closed.

The terms "quadrilateral" and "parallelogram" are used interchangeably, although strictly speaking they are not the same thing. A quadrilateral is simply a plane figure whose four edges are line segments. The word "quadrilateral" comes from **the Latin words** quadri- (four) + lamina (sheet). A parallelogram is a special type of quadrilateral where two pairs of opposite sides are parallel. A rectangle is a special case of a parallelogram where all four sides are equal in length.

If a quadrilateral is a parallelogram, then the angles that are adjacent are supplementary. When a quadrilateral is a parallelogram, opposing angles are congruent. If a quadrilateral is a parallelogram, its opposing sides must be congruent. If a quadrilateral is a parallelogram, the diagonals intersect. Two diagonal of a parallelogram intersect.

Thus, if a quadrilateral is a parallelogram, it can be proved to be congruent by showing that its opposite angles are equal and that one side is parallel to another.

For example, if a quadrilateral is a parallelogram with angles of 90 degrees, it can be proved to be congruent to another parallelogram by showing that both have equal opposing angles and that one side is parallel to another. The four conditions for proving two quadrilaterals are congruent are shown below:

1 Opposing angles are equal. (These angles are opposite each other.)

2 One side is parallel to another. (These sides are parallel or perpendicular to each other.)

3 Diagonals of a quadrilateral meet at a single point. (These diagonals connect two opposite angles.)

4 Quadrilateral is a parallelogram. (This condition does not apply to this problem.)

Rectangle A rectangle is a quadrilateral whose diagonals are equal and bisect each other. A standardized What is the significance of the quadrilateral being a parallelogram? The term quadrilateral means four-sided figure, and therefore a quadrilateral is any figure having four straight lines as sides. That is, it is a plane figure formed by connecting four distinct points that lie on one same line or line segment.

Thus, a quadrilateral is any plane figure with **four straight edges** or line segments as sides. A square is a special case of a quadrilateral; thus, a quadrilateral is any plane figure with four straight edges or line segments as sides including squares.

A rectangle is defined as a quadrilateral where two of the opposite angles are the same size and the other two angles are also the same size. Thus, a rectangle is a quadrilateral where there are two pairs of **parallel lines** and two pairs of perpendicular lines. A square is a special case of a rectangle where all four angles are the same size (90 degrees). A regular polygon is any number of sides regularity condition for polygons In mathematics, a polygon is regular if and only if it is symmetric with respect to each of **its axes** of symmetry.

Classification

- A quadrilateral is a polygon with four sides.
- A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals.
- A rhombus is a parallelogram with four congruent sides.
- A trapezoid is a quadrilateral with exactly one pair of parallel sides.