- Constructing a Bisector of an Angle
- Drawing a Perpendicular to a Line at a Point on the Line
- The Property of the Angle Bisectors of a Triangle
- Perpendicular Bisectors of the Sides of an Acute-angled Triangle
- Perpendicular Bisectors of the Sides of an Obtuse-angled Triangle
- Construct a Triangle Given the Lengths of Its Three Sides
- Construct a Triangle Given Two Sides and the Angle Included by Them
- Construct a Triangle Given Two Angles and the Included Side
- Construct a Right-angled Triangle Given the Hypotenuse and One Side
- Congruence Among Line Segments
- Congruence of Angles
- Congruence of Circles
Multiplication and Division of Integers
HCF and LCM
Angles and Pairs of Angles
Operations on Rational Numbers
- Concept of Rational Numbers
- Addition of Rational Number
- Additive Inverse of Rational Number
- Subtraction of Rational Number
- Multiplication of Rational Numbers
- Division of Rational Numbers
- Rational Numbers Between Two Rational Numbers
- Decimal Representation of Rational Numbers
- Bodmas Rules for Simplifying an Expression
- Concept of Exponents
- Concept of Square Number
- Concept of Cube Number
- Laws of Exponents
- Multiplying Powers with the Same Base
- Dividing Powers with the Same Base
- Taking Power of a Power
- Multiplying Powers with Different Base and Same Exponents
- Dividing Powers with Different Base and Same Exponents
- Numbers with Exponent Zero, One, Negative Exponents
- Miscellaneous Examples Using the Laws of Exponents
- Expressing Large Numbers in the Standard Form
- Finding the Square Root of a Perfect Square
Joint Bar Graph
Algebraic Expressions and Operations on Them
- Algebraic Expressions
- Terms, Factors and Coefficients of Expression
- Like and Unlike Terms
- Types of Algebraic Expressions as Monomials, Binomials, Trinomials Or Polynomials
- Addition of Algebraic Expressions
- Subtraction of Algebraic Expressions
- Multiplication of Algebraic Expressions
- Multiplying Monomial by Monomials
- Multiplying a Monomial by a Binomial
- Multiplying a Binomial by a Binomial
- Equations in One Variable
Direct Proportion and Inverse Proportion
Banks and Simple Interest
Perimeter and Area
Algebraic Formulae - Expansion of Squares
Arc of the Circle: A chord divides the circumference of a circle into two parts and each part is called an arc.
Minor Arc: The arc which is less than the semicircle is called minor arc.
Major Arc: The arc which is greater than the semicircle is called major arc.
Arc of the Circle:
An arc is a part of the circumference of a circle.
A chord divides the circumference of a circle into two parts and each part is called an arc.
In the figure, given above, chord PQ divides the circumference into two unequal arc PRQ and arc PQ.
The arc which is less than the semicircle is called minor arc.
The arc which is greater than the semicircle is called major arc.
If two arcs of a circle have common endpoints and the arcs make one complete circle, the arcs are said to be corresponding arcs. Here, arc PRQ and arc PQ are mutually corresponding arcs.
In the figure below, chord AB is a diameter of the circle. The diameter gives rise to two equal arcs. They are called semicircular arcs.