Quadrilateral

QUADRILAERALS
QUADRILATERALS – Quadrilateral is a union of four line segments determined by four distinct co-planar points of which no three are collinear and the line-segment intersect at end points.
Quadrilateral ABCD is denoted by □ABCD.
PARTS OF QUADRILATERAL: (□ABCD) Points A, B, C, D are called the vertices of □ABCD
AB, BC, CD and AD are called the sides of ABCD
AC, BD are called Diagonals of ABCD
A, B,C and D are the four angles of ABCD
A Quadrilateral has 10 parts – 4 line segments, 4 angles, 2 diagonals.
Sides of Quadrilateral are the subset of Quadrilateral.
Angels of Quadrilateral are not a subset of a Quadrilateral.
Diagonals of a Quadrilateral are not a subset of Quadrilateral.

ADJACENT SIDES: Two sides of a Quadrilateral intersecting in a vertex are called adjacent sides. E.g- AB and BC, BC and CD, CD and DA, DA and AB.

OPPOSITE SIDES: The sides of a Quadrilateral with no common end point are called opposite sides. E.g- AB and CD, AD and BC.

The intersection of opposite sides is null set.

ADJACENT ANGLES: A and B, B and C, C and D, D and A

OPPOSITE ANGLES: A and C, B and D

The Sum of the measures of all the angles of a Quadrilateral is 360.

TYPES OF QUADRILATERALS:-
1> Trapezium Parallelogram Rectangle Rhombus Square Kite
TRAPEZIUM
In a quadrilateral if only one pair of opposite sides are parallel to each other, then the Quadrilateral is called Trapezium.

Adjacent angles are supplementary to each other.
In trapezium if E and F are midpoints of AD and BC respectively,
EF = (AB + CD)
In a Trapezium if M and N are midpoint of Diagonals of trapezium then,
MN = |AB – CD|

PARALLELOGRAM
In a Quadrilateral, opposite sides are parallel to each other, then Quadrilateral is called Parallelogram.

In Parallelogram Opposite sides are congruent
In Parallelogram opposite angles are congruent.
Adjacent angles are congruent to each other.
In Parallelogram, diagonals bisect each other. Diagonals: – AC = AM = MC BD = BM = MD
It is denoted as □m

RECTANGLE

If all the angles of parallelogram are right angle, then the parallelogram is rectangle.
Diagonals of rectangle are equal. AC = BC
Every parallelogram is not rectangle, but every rectangle is parallelogram.

RHOMBUS

If all the sides of parallelogram are congruent, then the parallelogram is rhombus. AB = BC = CA = AD
Diagonals of rhombus bisect each other at right angle.
Diagonals bisect each other.
Every rhombus is a parallelogram.

SQUARE

If all the sides of rectangle are congruent then it is called square.
The diagonals of square are congruent and bisect each at right angle.
Every square is a parallelogram but every parallelogram is not square.
Every square is a rectangle but every rectangle is not square.
Every square is a rhombus, but every rhombus is not a square.

KITE

In kite AB = AD and BC = CD
The diagonals of kite are not congruent but intersect each other at right angle.
THE MIDPOINT THEOREM In triangle ABC- P, R, Q is midpoints of AB, BC, CA respectively. QR = ½ AB PR = ½ BC PQ = ½ AC
Perimeter of triangle ABC = 2 [Perimeter Of PQR]
Perimeter of Triangle PQR = ½ [Perimeter of ABC]

PROBABILITY
French mathematicians Pascal and Fermet initiated the concept of Probability in 17th Century.
TRIAL:- Trial is a action which results in more than one outcomes.
EVENT:- An Event for an experiment is the collection of some outcomes of an experiments. It is denoted by Capital letters.
PROBABILITY:- Probability of any event is given by the ratio of NO. of trials that event occurs to the total NO. of trials of the Experiments. Probability of Event A is denoted by P(A)
P(A)= Favorable outcomes/ Total NO. of outcomes
Probability of any event lies between 0 and 1 including both.

If probability any event is 0 then it is called impossible event.
If probability of any event is 1, then it is called SURE or CETAIN Event.
The sum of the probability of all disjoint or exhaustive Events is 1.
P(A) + P(A) = 1