Question

properties of trapezium,parallelogram,rectangle,rhombus, and square​

Answer 1

Step-by-step explanation:

Parallelogram:

As the name says, it must have something parallel. So, a parallelogram is a quadrilateral which has opposite sides parallel.

Property 1: The opposite sides of a parallelogram are of equal length i.e. AB = DC and BC = AD.

Property 2: The opposite angles of a parallelogram are of equal measure i.e. ∠A =∠C and ∠B = ∠D.

Property 3: The diagonals of a parallelogram bisect each other (at the point of their intersection) i.e. AE = CE and BE = DE.

So, these were properties of a parallelogram, quite easy!

Now, let’s get to the heir of the hierarchy i.e. Rectangle.

Rectangle:

A rectangle is a parallelogram with equal angles. So, this means a rectangle has inherited all the properties of a parallelogram and in addition to that it is having all angles equal.

Here, AB = CD and BC = AD.

And ∠A =∠B = ∠C = ∠D (All angles are equal)

Property 1: A rectangle is a parallelogram in which every angle is a right angle i.e. ∠A =∠B = ∠C = ∠D = 90°.

Property 2: The diagonals of a rectangle are of equal length i.e. AC = BD.

Property 3: The diagonals of a rectangle bisect each other (at the point of their intersection).

So, these were all properties of a rectangle being a parallelogram.

Rhombus:

A parallelogram with sides of equal length is called a rhombus.

So, as it says a rhombus is also a parallelogram which means it has also inherited all the properties of a parallelogram and it is having all sides equal other than that.

AB = BC = CD = DA (All sides are equal)

Property 1: All sides are of equal length i.e. AB = BC = CD = DA.

Property 2: The diagonals of a rhombus are perpendicular bisectors of one another i.e. AO = CO and BO = DO and ∠AOB =∠BOC = ∠COD = ∠DOA = 90°.

Now, we are left with the last one i.e. Square.

Square:

A rectangle with sides of equal length is called a square.

Since the square is the last one in the hierarchy, therefore, it must have all the properties of a parallelogram, rectangle, and rhombus.

So, to get the properties of a square just sum up all the properties you have learned so far.

Property 1: In a square, every angle is a right angle.

Property 2: The diagonals of a square are of equal length and perpendicular bisectors of each other.