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

  • solve problem-related relation between the pair of angles triangle.
  • solve problems of quadrilateral, trapezium, parallelogram, rectangle, rhombus and square.
  • solve problems related to similarity.
  • construct isosceles triangle  & quadrilateral triangle.
  • solve and manipulate the problems related to the tangent line of the circle.
  • solve problems of Trigonometric Ratios.
  • solve problem-related  experimental verification.



Triangles are three-sided closed figures which have three straight sides joined at three vertices and have three angles enclosed within the figure at the vertices. There are several types of triangles based on the lengths of its sides and the angles they contain. What many do not know is that a triangle is a three-sided polygon.


A closed figure formed by four straight lines on the same plane is called quadrilateral. Here, the properties are explained briefly with different theorem and converse of theorem. Parallelogram is a quadrilateral having opposite sides parallel.


Construct an isosceles triangle, quadrilateral and parallelogram having any base and remaining sides.


\(\triangle\)ABC and \(\triangle\)XYZ are similar i.e, \(\triangle\)ABC and \(\traingle\)XYZ have same shape but the size is different. If any two angles are equal to each other, then they are similar.


A closed curve line, lying in a plane, whose all points are equidistant from a fixed point in the same plane is called a circle. The symbol of the circle is "O". Diameters of circle divide the into two equal parts. The diameter is double of the radius and the radius is half of diameter. Every diameter of a circle is the longest chord of the circle. The distance between two concentric circles is the difference between the radii of those circle.