• A figure is said to have line symmetry, if by folding the figure along a line, the left and right parts of it coincide exactly. The line is called the line (or axis) of symmetry of the figure. A figure may have no line of symmetry, one line of symmetry, two lines of symmetry, three lines of symmetry and so on. Line symmetry is closely related to mirror reflection. The distance of the image of a point (or object) from the line of symmetry (mirror) is the same as that of the point from that line of symmetry. Many constructions can be made using different instruments of a geometry box

• A figure is said to have line symmetry, if by folding the figure along a line, the left and right parts of it coincide exactly. The line is called the line (or axis) of symmetry of the figure.  A figure may have no line of symmetry, one line of symmetry, two lines of symmetry, three lines of symmetry and so on. Line symmetry is closely related to mirror reflection. The distance of the image of a point (or object) from the line of symmetry (mirror) is the same as that of the point from that line of symmetry. Many constructions can be made using different instruments of a geometry box

• Ratio, Proportion and Unitary Method.  The comparison of two numbers or quantities by division is known as the ratio. Symbol ‘:’ is used to denote ratio. For a ratio, the two quantities must be in the same unit. If they are not, they should be expressed in the same unit before the ratio is taken. Two ratios are equivalent, if the fractions corresponding to themare equivalent. Four quantities are said to be in proportion, if the ratio of the first and the second quantities is equal to the ratio of the third and the fourth quantities. The symbol ‘::’ or ‘=’ is used to equate the two ratios. The order of terms in a proportion is…

• The word ‘variable’ means something that can vary, i.e., change. The value of a variable is not fixed. We use a variable to represent a number and denote it by any letter such as l, m, n, p, x, y, z etc. A variable allows us to express relation in any practical situation and to express many common rules and properties of geometry, algebra etc. An expression with a variable, constants and the sign of equality (=) is called an equation. The value of the variable which satisfies the equation is called a solution of the equation.

• Perimeter of a closed figure is the distance covered in one round along the boundary of the figure.  A closed figure in which all sides and angles are equal is called a regular polygon.  Perimeter of a rectangle = 2 × (length + breadth) Perimeter of a square = 4 × length of its side Perimeter of an equilateral triangle = 3 × length of a side The amount of region enclosed by a plane closed figure is called its area. Area of a rectangle = length × breadth Area of a square = side × side

• The data can be arranged in a tabular form using tally marks. A pictograph represents data through pictures of objects. Interpretation of a pictograph and drawing a pictograph. Representation of data using a bar diagram or bar graph. In a bar graph, bars of uniform width are drawn horizontally or vertically with equal spacing between them. Length of each bar gives the required information. Interpretation of a bar graph and drawing a bar graph.

• A fraction is a number representing a part of a whole. This whole may be a single object or a group of objects.  A fraction whose numerator is less than the denominator is called a proper fraction, otherwise it is called an improper fraction. Numbers of the type 541 3 ,8 ,2 795 etc. are called mixed fractions (numbers). An improper fraction can be converted into a mixed fraction and vice versa. Fractions equivalent to a given fraction can be obtained by multiplying or dividing its numerator and denominator by a nonzero number.  A fraction in which there is no common factor, except 1, in its numerator and denominator is called a fraction in the simplest or lowest form.…

• Main Concept And Result A fraction is a number representing a part of a whole. This whole may be a single object or a group of objects. A fraction whose numerator is less than the denominator is called a proper fraction, otherwise it is called an  improper fraction. Numbers of the type 541 3 ,8 ,2 795 etc. are called mixed fractions (numbers). An improper fraction can be converted into a mixed fraction and vice versa. Fractions equivalent to a given fraction can be obtained by multiplying or dividing its numerator and denominator by a nonzero number.  A fraction in which there is no common factor, except 1, in its numerator and denominator is called a fraction in…

• Main Concept And Result The collection of numbers 0, +1, –1, +2, –2, +3, –3, …… is called integers. The numbers +1, +2, +3, +4, ….. are referred to as positive integers. The numbers –1, –2, –3, –4, ……. are referred to as negative integers. The numbers 0, +1, +2, +3, …… are called non-negative integers. All the positive integers lie to the right of 0 and the negative integers to the left of 0 on the number line. All non negative integers are the same as whole numbers and hence all the opertations on them are done as in the case of whole numbers. To add two negative integers, we add the…

• Main Concepts And Results A line segment corresponds to the shortest distance between two points. The line segment joining points A and B is denoted as AB or as BA. A ray with initial point A and a point B on it is denoted as AB  Line AB is denoted as AB Two distinct lines in a plane that cross at a point are called intersecting lines, otherwise they are called parallel lines. Two rays with a common initial point form an angle. A simple closed curve made of line segments only is called a polygon. A polygon of three sides is called a triangle and that of four sides is called a quadrilateral. A polygon…

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