write 4 properties of each
(a) parallelogram
(b) rectangle
(c) square
(d) phambus
Answers
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.
Answer:
a) There are six important properties of parallelograms to know:
Opposite sides are congruent (AB = DC).
Opposite angels are congruent (D = B).
Consecutive angles are supplementary (A + D = 180°).
If one angle is right, then all angles are right.
The diagonals of a parallelogram bisect each other.
b) The fundamental properties of rectangles are:
A rectangle is a quadrilateral.
The opposite sides are parallel and equal to each other.
Each interior angle is equal to 90 degrees.
The diagonals bisect each other.
c) The diagonals of a square bisect each other and meet at 90°
The diagonals of a square bisect its angles.
Opposite sides of a square are both parallel and equal in length.
All four angles of a square are equal. ...
All four sides of a square are equal.
The diagonals of a square are equal.
d)Properties of Rhombus
All sides of the rhombus are equal.
The opposite sides of a rhombus are parallel.
Opposite angles of a rhombus are equal.
In a rhombus, diagonals bisecting each other at right angles.
Diagonals bisect the angles of a rhombus.
The sum of two adjacent angles is equal to 180 degrees