Maths

# Types of Quadrilateral and their Shapes

quadrilateral is a polygon that stands out for the characteristics of its sides and angles. This figure has four sides in total, also presenting four interior angles and four exterior angles.

These polygons come in a variety of shapes, but they all share the same characteristics: four vertices, four interior angles, four sides, two diagonals, and a sum of all angles equaling 360 degrees. Trapezoids, parallelograms, and trapezoids are the three types of figures. Parallelograms can be rhombus-shaped, square-shaped, rhomboid-shaped, or rectangle-shaped.

The sides that share a vertex are said to be consecutive.
The fact that opposite sides are equal and lack a common vertex distinguishes them.
The total of all the opposite sides of quadrilaterals becomes equal when they become constricted. AB + CD, for example, equals BC + DA.
Simple quadrilaterals are formed by joining two triangles with a common side that corresponds to one of the diagonals.
The angles of opposite angles and vertices are identical since they are not on the same side.
A rhombus is formed when the diagonals of a quadrilateral section are divided into four triangles with the same perimeter.
It has a midpoint where the diagonals connect.

A diagonal can only be drawn from a vertex.
The sum of the internal angles equals the sum of the four right angles, giving a total of 360 degrees.
Only one diagonal can be drawn starting from a vertex.
Angles on the same side that are next to each other become supplementary, meaning they add up to 180 degrees.
There are only two diagonals that can intersect at an inside position.

Interior angles.

The sum of all the interior angles of a quadrilateral gives a total of 360 degrees.

Parallelograms.

Quadrilaterals are considered parallelograms because they have two pairs of parallel opposite sides.

The quadrilateral will always be a parallelogram when its consecutive angles are supplementary, that is, the sum of its two angles equals 180 degrees. The sum of all interior angles equals 180 degrees. Likewise, the diagonals in this figure always bisect, that is, they are cut in half.

Trapezoids.

These figures do not have any pair of opposite parallel vertices, which is why certain quadrilaterals are considered to be trapezoids In isosceles trapezoids, their diagonals are always congruent, that is, they have the same length.

Rectangle.

It presents the equal opposite sides, its diagonals are equal and it presents all its equal angles. The diagonals in this figure always bisect and become congruent.

Diamond.

Its sides are equal, its opposite angles are equal, and the non-opposite angles are supplementary. These come to have perpendicular diagonals and present bisectors of the angles that they intersect.

The main diagonal of the rhomboid is the bisector of the angles it intersects and at the same time is the perpendicular bisector of the secondary diagonal.

Square.

It has all its sides and angles equal. Its diagonals are equal, perpendicular, and bisected.

There are different types of quadrilateral, which are classified into two classes based on their interior angles:

• Convex: all its interior angles are less than π radians (180º). The sum of its interior angles is 360º (2π radians) and its two diagonals are interior.
• Concave: one of its interior angles measures more than π radians (180º). At least one of its two diagonals is outside.
• Convex quadrilaterals can be divided into several categories based on their sides and angles :
• Parallelograms: is a quadrilateral that has the two pairs of opposite sides parallel and the opposite angles equal.
• Square: quadrilateral whose sides and angles are equal.
• Rectangle: it has four equal angles (90º) and equal sides two by two, the adjacent sides being different.
• Rhombus: all the sides are equal but the angles are different two by two so that the adjacent angles are different and each angle is equal to the non-adjacent angle.
• Rhomboid: has its sides and angles equal two to two. The rhomboid is also called a nonregular parallelogram.
• Trapezoids: a convex quadrilateral with two of its sides parallel and unequal.
• Rectangular trapezoid: it is characterized by having two parallel sides and two consecutive right angles (90º).
• Isosceles trapezoid: the angles are equal to two to two. It has two parallel sides and two oblique sides of equal length.
• Scalene trapezoid: all four interior angles are unequal.
• Trapezoids : is a quadrilateral in which no side is parallel to another.