Quadrilaterals

In geometry, a quadrilateral is a plane shape with four sides or edges and four corners or vertices. When we look around, many objects have a quadrilateral shape: the floor, walls, ceiling, classroom windows, kite, chessboard, and so on.

For a complete comprehension of geometry, it is necessary to grasp the notion of quadrilaterals. To assist you, we will go over definitions, formulas, types, shapes, and their attributes in depth in this article.

Quadrilateral

The term quadrilateral comes from two Latin words: quadri, which means four, and latus, which means sides. A quadrilateral is a two-dimensional shape with four sides, four angles, and four vertices (corners). A quadrilateral’s internal angles add up to 3600.

Things to know About Quadrilaterals

If A, B, C, and D are all coplanar points, then 

1. None of them are collinear.

2. When the line segments AB,BC,CD, and DA do not meet except at their endpoints, the resulting figure is called a quadrilateral (Abbreviation: quad).

3. The vertices are the points A, B, C, and D.

Adjacent Sides of Quadrilateral

The two sides of a quadrilateral that share a common end or vertex point are called adjacent sides. In the diagram above, there are four pairs of adjacent sides. (AB, BC), (BC, CD), (CD, DA), and (AB, BC) (DA, AB).

Opposite Sides of Quadrilateral

If a quadrilateral’s two sides do not have a common endpoint, they are called opposite sides. There are two pairs of opposite sides in the diagram above. (DA, CB) are the two (CD, BA).

Adjacent Angles of Quadrilaterals

The two angles of a quadrilateral with a shared arm are called adjacent angles. In the diagram above, there are four pairs of adjacent angles. The options are (D,A), (A,B), (B,C), and (C,D).

Opposite Angles of Quadrilateral

The opposite angles of a quadrilateral are the two angles that are not contiguous. There are two pairs of opposite angles in the diagram above. (∠A,∠C) and (∠B,∠D) are the two options.

The Interior and Exterior of a Quadrilateral

The quadrilateral ABCD divides all of the plane’s points into three portions, as seen in the diagram above.

The plane includes all points inside the quadrilateral, such as P, Q, and R. The inside portion of the quadrilateral is this area. All points such as P, Q, and R are included in the quadrilateral’s inner points.

All points outside of the quadrilateral, such as L, M, and N, are considered part of the plane. The quadrilateral’s outside section is referred to as such. The quadrilateral’s outer points are points like L, M, and N.

The interior of the quadrilateral is defined by its sides. There are also spots on the quadrilateral’s boundaries.

Types of Quadrilaterals

Quadrilateral figures come in many different sizes and shapes. Many more quadrilaterals can be easily drawn, and many of them are familiar to us.

Rectangle

A rectangle is a quadrilateral with opposite sides that are parallel and equal.

Properties of Rectangle

• All of the angles are right.

• All of the diagonals are the same length and cross each other (divide each other congruently).

• When two diagonals connect, opposite angles result.                                                 

Square

A square is a quadrilateral with all of its sides equal, or a special sort of parallelogram.

Characteristics of Square

• The sides and angles are all the same

• The diagonals are parallel

• The opposite sides are known as parallel sides

• The diagonals are perpendicular and cross each other                                               

Rhombus

A quadrilateral with four equal-length sides is known as a rhombus. For its equal length, it is often referred to as an equilateral quadrilateral.

Characteristics of Rhombus

• Each side is the same length

• Congruent angles are those that are perpendicular to each other

• The diagonals come together at a position that is perpendicular to one another

• Adjacent angles produce supplementary angles                                             

Trapezium

A trapezium is a quadrilateral that is convex in shape and has at least one pair of parallel sides.

Characteristics of Trapezium

• The bases of the trapezium are parallel to one another

• The diagonals will be congruent if the non-parallel sides are

• There are no sides, angles, or diagonals that are identical                                                   

Isosceles Trapezium

A quadrilateral with just one pair of opposite sides parallel to one another and all other pairs of sides congruent is called an isosceles trapezium.

An Isosceles Trapezium’s Characteristics

• Two adjacent angles are supplementary when they add up to 180 degrees

• It’s feasible to make a circle out of it

• The diagonals produce a pair of congruent triangles with equal sides as the base

• Four right angles are equal to the sum of the four outer and four interior angles

• Rotating an isosceles trapezium around the vertical axis that connects the midpoints of the parallel sides yields a cone fragment                                             

Parallelogram

A parallelogram is a quadrilateral with opposite parallel sides (and therefore opposite angles equal).

A parallelogram’s properties

• The opposite sides are known as parallel sides

• Congruent angles are those that are perpendicular to each other

• Interior angles on the same side are called successive angles

• Angles A and B, as well as angles D and C, are supplementary

• Each of a parallelogram’s diagonals divides it into two congruent triangles

• The diagonals of a parallelogram are bisected by each other                                             

Conclusion

We’ve covered some real-life quadrilateral instances, the definition of quadrilateral, and a few more facts regarding quadrilaterals in this post. We hope that reading the articles has given you a better grasp of quadrilaterals and geometry.

A quadrilateral is a two-dimensional closed shape with four sides, four corners, and four angles, the sum of which is 360 degrees.