Write all properties of Square, Rectangle, Rhombus, Parallelogram, Kite and Trapezium
Answers
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.
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Hey mate here is your answer
The properties of the figures you asked are as follows:
Square:
All four interior angles are equal to 90°
All four sides of the square are congruent or equal to each other
The opposite sides of the square are parallel to each other
The diagonals of the square bisect each other at 90°
The two diagonals of the square are equal to each other
The square has 4 vertices and 4 sides
The diagonal of the square divide it into two similar isosceles triangles
The length of diagonals is greater than the sides of the square.
Rectangle:
A rectangle is a quadrilateral
The opposite sides are parallel and equal to each other
Each interior angle is equal to 90 degrees
The sum of all the interior angles is equal to 360 degrees
The diagonals bisect each other
Both the diagonals have the same length
A rectangle with side lengths a and b has the perimeter as 2a+2b units
A rectangle with side lengths a and b has the area as: ab sin 90 = ab square units
The sum of the interior angles is equal to 360 degrees
A diagonal of a rectangle is a diameter of its circumcircle
If a and b are the sides of a rectangle, then the length of each diagonal is: d=a2+b2−−−−−−√
The diagonals bisect each other at different angles. One is acute, and another one is an obtuse angle
If the two diagonals bisect each other at right angles, then the rectangle is known as a square
A cylinder is obtained when the rectangle is rotated along the line joining the midpoint of the longer parallel sides. In this case, the height of the cylinder is equal to the width of a rectangle. Also, the cylinder diameter is equivalent to the length of a rectangle
A cylinder is obtained when the rectangle is rotated along the line joining the midpoint of the shorter parallel sides. In this case, the height of the cylinder is equal to the length of a rectangle. Similarly, the cylinder diameter is equivalent to the width of a rectangle
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 bisect each other at right angles.
Diagonals bisect the angles of a rhombus.
The sum of two adjacent angles is equal to 180 degrees.
The two diagonals of a rhombus form four right-angled triangles which are congruent to each other
You will get a rectangle when you join the midpoint of the sides.
You will get another rhombus when you join the midpoints of half the diagonal.
Around a rhombus, there can be no circumscribing circle.
Within a rhombus, there can be no inscribing circle.
You will get a rectangle, where the midpoints of the 4 sides are joined together, and the length and width of the rectangle will be half the value of the main diagonal so that the area of the rectangle will be half of the rhombus.
When the shorter diagonal is equal to one of the sides of a rhombus, two congruent equilateral triangles are formed.
You will get a cylindrical surface having a convex cone at one end and concave cone at another end when the rhombus is revolved about any side as the axis of rotation.
You will get a cylindrical surface having concave cones on both the ends when the rhombus is revolved about the line joining the midpoints of the opposite sides as the axis of rotation.
You will get solid with two cones attached to their bases when the rhombus is revolving about the longer diagonal as the axis of rotation. In this case, the maximum diameter of the solid is equal to the shorter diagonal of the rhombus.
You will get solid with two cones attached to their bases when the rhombus is revolving about the shorter diagonal as the axis of rotation. In this case, the maximum diameter of the solid is equal to the longer diagonal of the rhombus.
Parallelogram:
The opposite sides are congruent.
The opposite angles are congruent.
The consecutive angles are supplementary.
If anyone of the angles is a right angle, then all the other angles will be the right angle.
The two diagonals bisect each other.
Each diagonal bisects the parallelogram into two congruent triangles.
Kite:
The two angles are equal where the unequal sides meet.
It can be viewed as a pair of congruent triangles with a common base.
It has 2 diagonals that intersect each other at right angles.
The longer or main diagonal bisects the other diagonal.
A kite is symmetrical about its main diagonal.
The shorter diagonal divides the kite into 2 isosceles triangles.
Trapezium:
The parallel sides are called bases.
The other two non-parallel sides are called legs.
If the two non-parallel sides are equal and form equal angles at one of the bases, the trapezium is an isosceles trapezium.
Hope it helps!!!
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