Topics
Number Systems
Number Systems
Polynomials
Algebra
Coordinate Geometry
Linear Equations in Two Variables
Geometry
Coordinate Geometry
Introduction to Euclid’S Geometry
Mensuration
Statistics and Probability
Lines and Angles
- Introduction to Lines and Angles
- Basic Terms and Definitions
- Intersecting Lines and Non-intersecting Lines
- Introduction to Parallel Lines
- Pairs of Angles
- Parallel Lines and a Transversal
- Angle Sum Property of a Triangle
Triangles
- Concept of Triangles
- Congruence of Triangles
- Criteria for Congruence of Triangles
- Properties of a Triangle
- Some More Criteria for Congruence of Triangles
- Inequalities in a Triangle
Quadrilaterals
- Concept of Quadrilaterals
- Properties of a Quadrilateral
- Types of Quadrilaterals
- Another Condition for a Quadrilateral to Be a Parallelogram
- Theorem of Midpoints of Two Sides of a Triangle
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram
Circles
Areas - Heron’S Formula
Surface Areas and Volumes
Statistics
Algebraic Expressions
Algebraic Identities
Area
Constructions
- Introduction of Constructions
- Basic Constructions
- Some Constructions of Triangles
Probability
( a + b )2 = a2 + 2ab + b2 .
Notes
An algebraic identity is an algebraic equation that is true for all values of the variables occurring in it.
Identity I : `(x + y)^2 = x^2 + 2xy + y^2 `
Identity II : `(x – y)^2 = x^2 – 2xy + y^2`
Identity III : `x^2 – y^2 = (x + y) (x – y)`
Identity IV : `(x + a) (x + b) = x^2 + (a + b)x + ab`
Identity V : `(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx`
Remark : We call the right hand side expression the expanded form of the left hand side expression. Note that the expansion of `(x + y + z)^2` consists of three square terms and three product terms.
Identity VI :` (x + y)^3 = x^3 + y^3 + 3xy (x + y)`
Identity VII : `(x – y)^3 = x^3 – y^3 – 3xy(x – y) `
= `x^3 – 3x^2y + 3xy^2 – y^3`
Identity VIII : `x^3 + y^3 + z^3 – 3xyz = (x + y + z)(x^2 + y^2 + z^2 – xy – yz – zx)`
