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Class 9 Maths Definition Notes
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9th Class Math All Chapters Important Definition Notes
- Matrix: A rectangular layout or a formation of a collection of real numbers, say 0, 1, 2, 3, 4, and 7.
- Rectangular Matrix: A matrix M is called rectangular if, the number of rows of M ≠ the number of columns of M.
- Square Matrix: A matrix M is called a square matrix if, the number of rows of M = the number of columns of M.
- Row Matrix: A matrix is called a row matrix if M has only one row.
- Column Matrix: A matrix is called a column matrix if M has only one column.
- Null or Zero Matrix: A matrix M is called a null or uro matrix if each of its entries is 0.
- Diagonal Matrix: A square matrix M of the type is called a diagonal matrix of order 3-by-3, where all the three entries a, b,c are not zero i.e. at least one entry is non-zero.
- Sellar Matrix: A diagonal matrix M is Called a scalar matrix if all of its entries in the diagonal are the same.
- Scientific Notation: A number written in the form ax lOn, where 1 ~a< 10 and n is an integer, is called scientific notation.
- Characteristic: The integral part of the logarithm of any number is called the characteristic.
- Mantissa: The decimal part of the logarithm of a number is called the mantissa and is always positive.
- Rational Expression: The quotient p((x)) of two polynomials p(x) and q(x), where q(x) is a non-zero. qx polynomial: is called a rational expression.
- Surd: An irrational radical with rational radicand is called a surd.
- Coordinates of a Point: The real numbers x, y of the ordered pair (x, y) are called.
- Coordinates of a point P(x, y) in a plane. The first number x is called the x-coordinate (or abscissa) and the second number in (x, y) is called the y-coordinate (or ordinate) of the point P(x, y).
- Distance formula:
- Collinear or Non-collinear Points: Whenever two or more than two points happen to lie on the same straight line in the plane, they are called collinear points with respect to that line; otherwise they are called non-collinear.
- Equilateral Triangle: If the lengths of all three sides of a triangle are the same, then the triangle is called an equilateral triangle.
- Isosceles Triangle: Isosceles triangle PQR is a triangle that has two sides of equal length while the third side has a different length.
- Right Triangle: A right triangle is one in which one of the angles has a measure equal to 90°.
- Pythagoras’ Theorem: In a right angle triangle ABC, IABl2 = IBCl2 + ICAl2, where LACB = 90°
- Scalene Triangle: A triangle is called a scalene triangle if the measures of all three sides are different.
- Square: A square is a closed figure in the plane formed by four non-collinear points such that the lengths of all sides are equal and the measure of each angle is 90°.
- Parallelogram: A figure formed by four non-collinear points in the plane is called a parallelogram if
- (i) its opposite sides are of equal measure
- (ii) its opposite sides are parallel
- Congruent Triangles: Two triangles are said to be congruent (symbol) if there exists a correspondence between them such that all the corresponding sides and angles are congruent.
- S.A.S. Postulate: In any correspondence of two triangles, if two sides and their included angle of one triangle are congruent to the corresponding two sides and their included angle of the other, then the triangles are congruent.
- Right Bisector of a Line Segment: A line l is called a right bisector of a line segment if l is perpendicular to the line segment and passes through its mid-point.
- Angle Bisector: Angle bisector is the ray that divides an angle into two equal parts.
- Similar Triangles: Two (or more) triangles are called similar (symbol -) if they are equiangular and measures of their corresponding sides are proportional.
- Concurrent Lines: Three or more than three lines are said to be concurrent if they all pass through the same point. The common point is called the point of concurrency of the lines.
- Incentre of a Triangle: The internal bisectors of the angles of a triangle meet at a point called the Incentre of the triangle.
- Circumcentre of a Triangle: The point of concurrency of the three perpendicular bisectors of the sides of a triangle is called the circumcentre of the triangle.
- Median of a Triangle: A line segment joining a vertex· of a triangle to the mid-point of th,e opposite side -is called a median of the triangle.
- Altitude of a Triangle: A line segment from a vertex of a triangle, perpendicular to the line containing the opposite side, is called an altitude of the triangle.
- Orthocentre of a Triangle: The point of concurrency of the three altitudes of a ~ is called its orthocentre.
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