#### Topics

##### Number Systems

##### Number Systems

##### Algebra

##### Polynomials

##### Linear Equations in Two Variables

##### Algebraic Expressions

##### Algebraic Identities

##### Coordinate Geometry

##### Geometry

##### Introduction to Euclid’S Geometry

##### Lines and Angles

##### 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
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Another Condition for a Quadrilateral to Be a Parallelogram
- The Mid-point Theorem
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- 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

##### Area

##### 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

##### Constructions

##### Mensuration

##### Areas - Heron’S Formula

##### Surface Areas and Volumes

##### Statistics and Probability

##### Statistics

##### Probability

#### notes

Heron was born in about 10AD possibly in Alexandria in Egypt. He worked in applied mathematics. His geometrical works deal largely with problems on mensuration written in three books. In this book, Heron has derived the famous formula for the area of a triangle in terms of its three sides.

The formula given by Heron about the area of a triangle, is also known as Hero’s formula. It is stated as:

Area of a triangle = `sqrt (s(s-a) (s - b)(s-c))` |

where a, b and c are the sides of the triangle, and s = semi-perimeter, i.e., half the perimeter of the triangle = `(a + b + c) /2`,

For instances, Let us take a = 40 m, b = 24 m, c = 32 m,

so that we have s = `(40 + 24 + 32 )/ 2` m

= 48 m

s - a = (48 - 40) m = 8m

s - b = (48 - 24)m = 24 m

s - c = (48 - 32 ) m = 16 m

Therefore, area of the park ABC

`= sqrt (s(s - a) (s - b) (s - c))`

`= sqrt (48 * 8 * 24 * 16) m^2 = 384 m^2`

#### description

- Collinearity of three points