PROPERITES OF QUADRILATERAL
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A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.
Sum of interior angles of a quadrilateral is 360.
There are six types of quadrilaterals. They are
Parallelogram
Definition of parallelogram :
A parallelogram is a quadrilateral which has opposite sides parallel.
Properties of parallelogram :
- Opposite sides are equal in length
- Opposite angles are equal in size.
- Diagonals bisect each other.
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Rectangle
Definition of rectangle :
A rectangle is a parallelogram with four equal angles of 90 degree.
Properties of rectangle :
- Opposite sides are equal and parallel.
- Diagonals bisect each other.
- Diagonals are equal in length.
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Rhombus
What is rhombus ?
A rhombus is a quadrilateral in which all sides are equal is length.
Properties :
- Opposite sides are parallel.
- Opposite angles are equal in size.
- Diagonals bisect each other at right angles.
- Diagonals bisect the angles at the vertex.
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Square
What is square ?
A square is a rhombus with four equal angles of 90.
Properties :
- Opposite sides are parallel.
- All sides are equal in length.
- Diagonals bisect each other at right angles.
- Diagonals bisect the angles at each vertex.
- Diagonals are equal in length.
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Trapezium
What is trapezium ?
A trapezium is a quadrilateral which has a pair of parallel opposite sides.
Properties :
- A trapezium has two parallel sides and two non parallel sides.
- The diagonal of regular trapezium bisect each other.
- The length of the midsegment is equal to half the sum of parallel bases.
- Two pairs of adjacent angles of a trapezium formed between the parallel sides and one of the non parallel side, add up to 180 degrees.
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Kite
Definition of kite :
A kite is a quadrilateral which has two pairs of adjacent sides equal in length.
Properties :
- One diagonal is an axis of symmetry.
- One pair of opposite angles are equal.
- Diagonals cut each other at right angles.
- One diagonal bisect one pair of angles at vertices.
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Properties of Quadrilaterals Quiz
Which of the following are true? Give reason for your answers.
Problem 1 :
A rectangle is a quadrilateral.
Solution :
True, since it has four sides, we can say rectangle is a quadrilateral.
Problem 2 :
A rectangle is a square.
Solution :
A rectangle may be a square sometimes, if all sides are equal. So, it is true.
Problem 3 :
A square is a rhombus.
Solution :
True, since all sides are equal in square and in rhombus.
Problem 4 :
A rhombus is a parallelogram.
Solution :
True, since opposite sides are parallel, we say rhombus is a parallelogram.
Quiz on properties of quadrilaterals
Problem 5 :
Find x in the following figure.
Solution :
∠1 = 90
Sum of exterior angles = 360
90 + ∠1 + 60 + x + 40 = 360
90 + 90 + 60 + x + 40 = 360
280 + x = 360
x = 360 - 280
x = 80
So, the missing angle measure is 80 degree.
Problem 6 :
Two adjacent angles of a parallelogram are in the ratio 4:5. Find their measures.
Solution :
Angles of parallelogram = 4x and 5x
Sum of adjacent angles = 180
4x + 5x = 180
9x = 180
x = 180/9
x = 20
4(20) ==> 80
5(20) ==> 100
So, the required angle measures are 80 and 100.
Problem 7 :
In the figure, HOPE is a rectangle. Its diagonals meet at G. If HG = 5x + 1 and EG = 4x + 19, find x.
Solution :
Since it is rectangle, the diagonals will bisect each other.
EG = GO
HG = GP
4x + 19 = 5x + 1
4x - 5x = 1 - 19
-x = -18
x = 18
So, the value of x is 18.
Problem 8 :
RICE is a rhombus. Find x, y, z. Justify your findings. Hence, find the perimeter of the rhombus
Solution :
EO = OI
5 = x + 2
x = 5 - 2
x = 3
12 = y + x
Applying the value of x, we get
12 = y + 3
y = 12 - 3
y = 9
So, the values of x and y are 3 and 9 respectively.
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