Write the properties of parallelogram,rhombus,rectangle,square,trapezium and kite.
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Answer:-Parallelogram:
As the name says, it must have something parallel. So, a parallelogram is a quadrilateral which has opposite sides parallel.
Properties:-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!
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.
Properties:-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.
Properties:-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°.
Square:
A rectangle with sides of equal length is called a square.
Properties:-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.
Trapezium:-
trapezium or a trapezoid is a quadrilateral with a pair of parallel sides. A parallelogram may also be called a trapezoid as it has two parallel sides. The pair of parallel sides is called the base while the non-parallel sides are called the legs of the trapezoid. The line segment that connects the midpoints of the legs of a trapezoid is called the mid-segment
Every trapezium shows the following properties:
Angle: The sum of angles in a trapezoid-like other quadrilateral is 360°. So in a trapezoid ABCD, ∠A+∠B+∠C+∠D = 360°.
Two angles on the same side are supplementary, that is the sum of the angles of two adjacent sides is equal to 180°.
Its diagonals bisect with each other.
The length of the mid-segment is equal to 1/2 the sum of the bases. In the above figure mid-segment= 1/2 (AB+CD)
In special cases of the isosceles trapezium, legs of the trapezium are congruent to each other. This means that despite being non-parallel, the measurement of both the legs is equal.
Kite:-
Kite is also a quadrilateral as it has four sides. Being a special type of quadrilateral, it shows special characteristics and properties which are different from the other types of quadrilaterals. A kite is the combination of two isosceles triangles.
•In a kite, two adjoining sides are equal
These sides are called as distinct consecutive pairs of equal length. From the above discussion we come to know about the following properties of a kite:
•Two pairs of sides known as consecutive sides are equal in length.
•One pair of diagonally opposite angles is equal in measurement. These angles are said to be congruent with each other.
•The diagonals meet each other at 90°, this means that they form a perpendicular bisection.
