### Properties of Rectangles

We see different kind of shapes around us all the time. Some are geometrical, some are not, some are 2 dimensional and some are 3 dimensional and so on. The rectangle is one of the important and interesting shapes that is studied in geometry. It is a four-sided polygon with straight sides, a flat shape and with four right angles. The rectangle is one of the common geometric shapes we find in our daily life. All the daily things we use, like a table, books, mobile phones, magazines, TV screen, etc. all are rectangles.

A rectangle can be defined as a four-sided quadrilateral with all its four angles being 90°. A rectangle with all sides equal to each other is called as a square. A rectangle is also a parallelogram but a special parallelogram, with equal angles.

Now let us learn the properties of a rectangle. Rectangles have all the properties of a parallelogram because at the end it is a parallelogram. But what makes rectangle special are the extra properties apart from the properties of a parallelogram. In a rectangle, all the angles are equal and equal to 90 degrees. The diagonals of a rectangle are equal which is not equal in case of a parallelogram. In a parallelogram, diagonals are just bisectors, in a rhombus diagonal are perpendicular bisectors. The diagonals of a rectangle are congruent.

*Some properties of rectangles are mentioned in the points below.*

- A rectangle is a parallelogram with 4 right angles
- Each of the interior angles of a rectangle is 90° making the sum of interior angle to be 360°.
- The diagonals of a rectangle bisect each other.
- The opposite sides of a rectangle are parallel.
- The opposite sides of a rectangle are equal.
- A rectangle whose side lengths are a and b has area ab sin 90° = ab.
- A rectangle whose side lengths are a and b has perimeter 2a + 2b
- Each diagonal of a rectangle is a diameter of its circumcircle.

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**Video Transcription **

Next we look at rectangles, so what is a rectangle? Rectangle is also a parallelogram, but a special parallelogram, with equal angles. Now we know that rhombus is with equal sides, rhombus is a parallelogram with equal sides, rectangle is a parallelogram with equal angles. So a rectangle will look like this, where all four angles are equal, because of which all of them will be equal to 90 degree also because you know that sum of the angles in a quadrilateral is 360, if all of them are equal, each one of them will be equal to 90 degree. Now properties wise, for a rectangle what are the properties? All properties of a parallelogram right? Rectangles will have all the properties of a parallelogram because finally it is a parallelogram. Apart from that why it is a special parallelogram because of this extra properties which is all the angles are equal and equal to 90 degree that is an important word, one more the diagonals that is these two diagonals in this rectangle, diagonals will be equal. In a parallelogram diagonals are just bisectors, in a rhombus diagonals are perpendicular bisectors, you know they are bisectors and equal. So in rectangle, diagonals are equal, in arhombus diagonals are perpendicular bisectors and in a parallelogram, they are just bisectors. Now we have understood what is a rhombus. Rhombus is where all sides are equal. We understood what is a rectangle, where all angles are equal and equal to 90 degree. Now let us look at a scenario where both this conditions are satisfied that is firstly I will show a rhombus here, here all sides are equal. Here I will take a rectangle, where all the angles are equal. Now all side both of them are parallelograms now what will happen? What will be the kind od parallelograms where both of these qualities added both the sides are equal and angles are equal if you bring together, you will end up getting a square like this. So what is a square? A square is parallelogram where sides are equal and angles are equal. Where only sides are equal it’s called a rhombus, when angles are equal it is called a rectangle. When both will happen that is when sides are equal and angles are equal, that kind of parallelogram will be square. So it is obvious that a square will have properties of a parallelogram, because finally it is a parallelogram. Love the properties of a parallelogram, love the properties of a rhombus love the properties of a rectangle. So it is very easy to understand or it is obvious that __ what about diagonals? What will be the properties of the diagonals of a square? very simple right? Diagonals will bisect each other as in a parallelogram because you know that in a parallelogram , diagonals bisect each other. In rhombus, diagonals are perpendicular to each other in a rectangle, diagonals are equal. So in a square, all these qualities will be there. Diagonals will bisect each other like in a parallelogram, or because it it’s a parallelogram ,because square is a parallelogram they will be of equal length because square is a rectangle also, and they are perpendicular to each other because square is a rhombus also