Mathematics is the base of human civilization. From cutting vegetables to arranging books on the shelves, from tailoring clothes to motion of Planets - Mathematics applies everywhere.
If A, B, C and D are four points in a plane such that no three of them are collinear and the line segments AB, BC, CD and DA do not intersect except at their end points, then the closed figure made up of these four line segments is called a quadrilateral with vertices A, B, C and D.
Two figures, which have the same shape and same size are called congruent figures and this property is called congruence. Congruent figures, when placed one over another, exactly coincide with one another or cover each other. In other words, two figures will be congruent, if parts of one figure are equal to the corresponding parts of the other.
Triangle is the simplest polygon of all the closed figures formed in a plane by three line segments. It is a closed figure formed by three line segments having six elements - three angles (i) ∠ABC or ∠B (ii) ∠ACB or ∠C (iii) ∠CAB or ∠A and three sides - (iv) AB (v) BC (vi) CA.
A set is well defined collection of distinct objects (also called as elements). Sets are conventionally denoted with capital letters. The elements of the sets are denoted by small letters. Sets A and B are equal if and only if they have precisely the same elements.
A sequence is an arrangement of a number in a definite order according to some rule. A sequence containing a finite number of terms is called a finite sequence. Let a1, a2, a3, ... be the sequence, then the sum expressed as a1+a2+a3+ ... is called series.
The ratio of two qualities a and b in the same units, is the fraction a/b and we write it as a:b. In the ratio, a:b, we call a as the first term of antecedent and b, the second term consequent. For example, the ratio 5:9 represents 5/9 with antecedent 5 and consequent 9.
Expressions are formed from variables and constants. Terms are added to form expressions. Expressions that contain exactly one, two and three terms are called monomials, binomials and trinomials respectively. In general, any expression containing one or more terms with non-zero coefficients (and with variables having non-negative exponents) is called a polynomial.
A fraction is a part of the whole (object, thing, region). For example, 5/12 is a fraction. Here 12 is the number of equal part into which the whole has been divided, is called denominator and 5 is the number of equal parts which have been taken out, is called numerator.
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