Properties of Quadrilaterals

 

Properties of Quadrilaterals

Let us understand in a better way with the help of an example:



  • It has four sides: AB, BC, CD, and DA
  • It has four vertices: Points A, B, C, and D
  • It has four angles: ∠ABC, ∠BCD, ∠CDA, and ∠DAB
  • ∠A and ∠B are adjacent angles
  • ∠A and ∠C are the opposite angles
  • AB and CD are the opposite sides
  • AB and BC are the adjacent sides

A quadrilateral is a 4-sided plane figure. Below are some important properties of quadrilaterals :

  • Every quadrilateral has 4 vertices, 4 angles, and 4 sides
  • The total of its interior angles = 360 degrees

Square Properties

  • All the sides of the square are of equal measure
  • The sides are parallel to each other
  • All the interior angles of a square are at 90 degrees (i.e., right angle)
  • The diagonals of a square perpendicular bisect each other


Rectangle Properties

  • The opposite sides of a rectangle are of equal length
  • The opposite sides are parallel to each other
  • All the interior angles of a rectangle are 90 degrees.
  • The diagonals of a rectangle bisect each other.


Rhombus Properties

  • All the four sides of a rhombus are of the same measure
  • The opposite sides of the rhombus are parallel to each other
  • The opposite angles are of the same measure
  • The sum of any two adjacent angles of a rhombus is equal to 180 degrees
  • The diagonals perpendicularly bisect each other


Parallelogram Properties

  • The opposite side of the parallelogram are of the same length
  • The opposite sides are parallel to each other
  • The diagonals of a parallelogram bisect each other
  • The opposite angles are of equal measure
  • The sum of two adjacent angles of a parallelogram is equal to 180 degrees


Properties of Trapezium

  • Only one pair of the opposite side of a trapezium is parallel to each other
  • The two adjacent sides of a trapezium are supplementary (180 degrees)
  • The diagonals of a trapezium bisect each other in the same ratio


Properties of Kite

  • The pair of adjacent sides of a kite are of the same length
  • The largest diagonal of a kite bisect the smallest diagonal 
  • Only one pair of opposite angles are of the same measure.

A glance at the Quadrilateral Properties

Quadrilaterals and its properties

Sides and Angles of Quadrilaterals

Sides and anglesSquareRectangle Rhombus ParallelogramTrapezium
All sides are equalYesNoYesNoNo
Opposite sides are parallelYesYesYesYesYes
Opposite sides are equalYesYesYesYesNo
All the angles are of the same measureYesYesNoNoNo
Opposite angles are of equal measureYesYesYesYesNo
Diagonals bisect each otherYesYesYesYesNo
Two adjacent angles are supplementaryYesYesYesYesNo

Comments

Post a Comment

Popular posts from this blog

Fibonacci Sequence

Image
  Fibonacci Sequence The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The next number is found by adding up the two numbers before it: the 2 is found by adding the two numbers before it (1+1), the 3 is found by adding the two numbers before it (1+2), the 5 is (2+3), and so on! Example: the next number in the sequence above is 21+34 =   55 It is that simple! Here is a longer list: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, ... Makes A Spiral When we make squares with those widths, we get a nice spiral: Do you see how the squares fit neatly together? For example 5 and 8 make 13, 8 and 13 make 21, and so on. This spiral is found in nature! See:  Nature, The Golden Ratio, and Fibonacci The Rule The Fibonacci Sequence can be written as a "Rule" (see  Sequences and Series ). First, the terms are numbered from 0 onwards like this: n = 0 1 2 3
Read more

Circle

Image
  Circle   A circle is easy to make: Draw a curve that is "radius" away from a central point. And so: All points are the same distance from the center. You Can Draw It Yourself Put a pin in a board, put a loop of string around it, and insert a pencil into the loop. Keep the string stretched and draw the circle!   The  Radius  is the distance from the center outwards. The  Diameter  goes straight across the circle, through the center. The  Circumference  is the distance once around the circle. And here is the really cool thing: When we divide the circumference by the diameter we get 3.141592654... which is the number  π  ( Pi ) So when the diameter is 1, the circumference is 3.141592654...   We can say: Circumference =  π  × Diameter Example: You walk around a circle which has a diameter of 100m, how far have you walked? Distance walked = Circumference =  π  × 100m =  314m  (to the nearest m) Also note that the Diameter is twice the Radius: Diameter = 2 × Radius And so this is
Read more