#### 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

- Collinearity of three points

## 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`