# Basic Geometry

The term ‘Geometry’ is the English equivalent of the Greek word ‘**Geometron**’. ‘Geo’ means Earth and ‘metron’ means Measurement. According to historians, the geometrical ideas shaped up in ancient times, probably due to the need in art, architecture and measurement. These include occasions when the boundaries of cultivated lands had to be marked without giving room for complaints.

Construction of magnificent palaces, temples, lakes, dams and cities, art and architecture propped up these ideas. Even today geometrical ideas are reflected in all forms of art, measurements, architecture, engineering, cloth designing, etc. You observe and use different objects like boxes, tables, books, the ball with which you play and so on. All such objects have different shapes. The pictures of a bangle, the one rupee coin or a ball appear round.

### Points

A point determines a location. If you mark three points on a paper, you would be required to distinguish them. For this they are denoted by a single capital letter like A, B, C. These points will be read as point A, point B and point C.

### Line Segment

A line segment has two end points A and B. Mark any two points A and B on a sheet of paper. Try to connect A to B by all possible routes. The shortest join of point A to B (including A and B) is a line segment. The points A and B are called the **end points** of the segment.

### Line

Imagine that the line segment from A to B is extended beyond A in one direction and beyond B in the other direction without any end. A line through two points A and B extends

indefinitely in both directions. So it contains a countless number of points. A line is denoted by a letter like l, m.

**Intersecting Lines**

If two lines have one common point, they are called intersecting lines. For example, the letter X of the English alphabet; crossing roads.

**Parallel Lines**

Lines which do not meet are said to be parallel and are called parallel lines. For example, the opposite edges of ruler (scale), railway lines.

### Ray

A ray is a portion of a line. It starts at one point (called starting point or initial point) and goes endlessly in a direction. For example, a ray of light from a torch.

### Curves

When you draw some drawings without lifting the pencil from the paper and without the use of a ruler, you get curves. If a curve does not cross itself, then it is called a **simple curve**.

In a **closed curve**, there are three parts:

- Interior (inside) of the curve
- Boundary (on) of the curve
- Exterior (outside) of the curve

For example, a court line in a tennis court divides it into three parts: inside the line, on the line and outside the line. You cannot enter inside without crossing the line. The interior of a curve together with its boundary is called its **region**.

### Polygon

A figure is a **polygon** if it is a simple closed figure made up entirely of line segments. The line segments forming a polygon are called its **sides**. The meeting point of a pair of sides is called its **vertex**. Any two sides with a common end point are called the **adjacent sides** of the polygon. The end points of the same side of a polygon are called the **adjacent vertices**.

### Angles

Angles are made when **corners** are formed. An angle is made up of two rays starting from a common initial point. The two rays forming the angle are called the **arms or sides** of the angle. The common initial point is the **vertex** of the angle.

### Triangles

A triangle is a three-sided polygon. It is the polygon with the least number of sides. In ∆ABC, the three **sides** of the triangle are AB, BC and CA. The three **angles** are ∠BAC , ∠BCA and ∠ABC. The points A, B and C are called the **vertices** of the triangle.

Being a polygon, a triangle has an exterior and an interior.

### Quadrilaterals

A four sided polygon is a quadrilateral. It has 4 sides and 4 angles. This quadrilateral ABCD has four sides AB, BC, CD and DA. It has four angles ∠A, ∠B, ∠C and ∠D.

In any quadrilateral ABCD, AB and BC are **adjacent sides**. AB and DC are **opposite sides**. ∠A and ∠C are said to be **opposite angles**. Similarly, ∠D and ∠B are opposite angles. Naturally, ∠A and ∠B are **adjacent angles**.

### Circles

You find many things that are round, a wheel, a bangle, a coin, etc. A circle is a simple closed curve which is not a polygon. It has some very special properties.

Every point on the circle is at equal distance from the **centre**. The **radius** is a line segment that connects the centre to a point on the circle.

A **chord** of a circle is a line segment joining any two points on the circle. A **diameter** is a chord passing through the centre of the circle.

A region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides is called a **sector**.

A region in the interior of a circle enclosed by a chord and an arc is called a **segment** of the circle.

The distance around a circle is its **circumference**.

A diameter of a circle divides it into two equal parts - each part is a **semi-circle**. A semi-circle is half of a circle, with the end points of diameter as part of the boundary.