This section starts with a brief introduction of geometric figures and their types. It explains in detail plain geometric figure - the quadrilateral. It also explains various types of quadrilaterals in terms of their definitions and properties. The section then goes on to explain circles and their features and concludes with three-dimensional figures.

Section 1: Objectives

Students will be able to:

1. define geometric figures and their types.
2. explain various types of quadrilaterals, their types and properties.
3. explain circles and their features.
4. define three-dimensional figures - cuboid, cube and pyramid.

Topic 1.1  Geometrical Figures

In Geometry-I, we learned what point, line, line segment and plane are. Now let us learn about geometric figures.

Closed figures made by the combination of line segments are known as “Geometric Figures”.

Geometric figures are of two types.

     1. Plane Geometric Figures or two-dimensional Figures
     2. Pictorial Figures or three-dimensional Figures

Plane geometric figures:

Plane Geometric figures are points, lines, line segments, triangles, quadrilaterals, circles, etc. In this section, we will learn more about quadrilaterals.

Definition of quadrilateral:

A quadrilateral is a simple closed figure formed by four line segments such that no two line segments cross each other except at their end points as shown.

The quadrilateral formed by the four bounding line segments AB, BC, CD and DA is named Quadrilateral ABCD.

• The four line segments AB, BC, CD and DA are called its sides and the four points A, B, C, D its vertices.
  
  
• A quadrilateral has four angles.
  
  
• In the above figure DAB, ABC, BCD and CDA are the four angles of the quadrilateral ABCD.
  
  
• They may be briefly written as A, B, C and D respectively.

Let us consider ABCD whose sides are AB, BC, CD and DA. The sum of the lengths of its sides, namely, AB + BC + CD + DA is called the perimeter of the quadrilateral.

• Also, AB and BC are the two adjacent sides of the quadrilateral.
  
  
• Again, A and B are the two adjacent angles of the quadrilateral.
  
  
• In the same way, B and C, C and D, D and A are the adjacent angles.
  
  
• The sides AB and CD are called opposite sides.
  
  
• Similarly BC and AD are the other two opposite sides.
  
  
• The line segment joining any two opposite vertices is called ‘diagonal’.
  
  
• In the figure AC is diagonal of the quadrilateral. Similarly BD is the other diagonal.

We see that:

        1. A quadrilateral has four sides, four angles and two diagonals.
        2. The sum of the angles of a quadrilateral is 360°.

Example 1:

In a quadrilateral, three of its angles are 55°, 65° and 105°. What is the fourth angle?

The sum of the four angles of a quadrilateral is 360°.

The sum of the given three angles = 55° + 65° + 105° = 225°

Therefore, the fourth angle = 360°- 225° = 135°

Example 2:

In a quadrilateral, two angles are 80° and 120°. The remaining two angles are equal. What is the measure of each of these angles?

Sum of the given angles = 80° + 120° = 200°

The sum of the four angles of the quadrilateral is 360°

Therefore, sum of the remaining two angles
                = 360°- 200° = 160°

But as they are equal,
each angle will therefore be = ½ of 160° = 80°.