#### Topics

##### Number Systems

##### Number Systems

##### Algebra

##### Polynomials

##### Linear Equations in Two Variables

##### Coordinate Geometry

##### Geometry

##### Coordinate Geometry

##### Mensuration

##### Introduction to Euclid’S Geometry

##### Lines and Angles

- Introduction to Lines and Angles
- Basic Terms and Definitions
- Intersecting Lines and Non-intersecting Lines
- Parallel Lines
- Pairs of Angles
- Parallel Lines and a Transversal
- Lines Parallel to the Same Line
- Angle Sum Property of a Triangle

##### Statistics and Probability

##### Triangles

##### Quadrilaterals

- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Angle Sum Property 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

- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Angle Subtended by a Chord at a Point
- Perpendicular from the Centre to a Chord
- Circles Passing Through One, Two, Three Points
- Equal Chords and Their Distances from the Centre
- Angle Subtended by an Arc of a Circle
- Cyclic Quadrilateral

##### 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} = a^{2} + 2ab + b^{2} .

## 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`

**`x^2 – y^2 = (x + y) (x – y)`**

Identity III :

Identity III :

**`(x + a) (x + b) = x^2 + (a + b)x + ab`**

Identity IV :

Identity IV :

**`(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx`**

Identity V :

Identity V :

**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.**

Remark :

Remark :

**Identity VI :**` (x + y)^3 = x^3 + y^3 + 3xy (x + y)`

**`(x – y)^3 = x^3 – y^3 – 3xy(x – y) `**

Identity VII :

Identity VII :

= `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)`