#### Geometry

After completion of this chapter, students will be able to:

- prove the theorems related to area of quadrilateral and triangle.
- solve and manipulate the problems involving the theorems of area of quadrilateral and triangle.
- verify the theorems on circle experimentally.
- prove the theorems on circle.
- solve and manipulate the problems related to the tangent line of the circle.
- construct quadrilateral and triangle which are related to area.

#### Notes

#### Area of Triangle and Quadrilateral

The triangle is a three-sided polygon and quadrilateral are four sided polygon. Since triangle and quadrilateral are both closed plane figures, they divide the plane into the interior and exterior regions. The notation of area of triangle and quadrilateral, used in daily life always means that measure of the extent of the interior region.

#### Construction

The theorems related to the area of a triangle is half of parallelogram standing on the same base and between same parallels, the area of parallelograms on the same base and between the same parallels are equal and so on.

#### Circle

A 2-dimensional shape made by drawing a curve that is always the same distance from a centre.

#### Experimental Verification

Therefore, the area of a triangle is equal to half of the area of the parallelogram on the same base and between the same parallel lines.