**Objective** of the chapter:** Geometry - Class 4**

In the 4th Grade Geometry chapter, you will learn about:

*point, line segments, ray**angles and types of angles**triangles, quadrilaterals and circles*

## 4th Grade Geometry

**Point:** A point is a very small dot made with a pencil. They have neither size nor dimension. A capital letter is used to name a point.

See the image given below. This is **point O**.

### Line Segment

**Line segment:** A line segment is a straight path between two points.

Below image is an example of a line segment. This line segment is called **line segment AB**.

A line segment extending endlessly on both sides is called a **line**. It does not have a beginning or an end.

In the below image, we have drawn a line segment XY. Let extend XY on both sides and add two arrow marks on either end.

This represents a line XY.

**Ray:** A ray is a part of a line which extends endlessly in one direction only.

Draw a line segment PQ and extend it in one direction only. Put an arrow mark at that end. This represents a **ray PQ**. See the image given below.

**Measuring line segments**

We use a ruler to measure the length of the line segment.

Follow the below **rule **to measure the line segment with a ruler:

- Place the ruler along the line segment.
- Adjust the ruler such that its '0' mark coincides with one end of the line segment.
- Read the mark on the ruler at the other end of the line segment.
- This gives the length of the line segment.

### Angles

In geometry, an angle can be defined as the figure formed by two rays meeting at a common end point.

Thus, when two rays meet at a point, an angle is formed.

See the image given below. The angle is formed by *ray OA* and *ray OB*, with a common endpoint B.

The two rays forming the angle are called the *arms of the angle*. Ray OA and ray OB are the arms of the angle.

The common point O is called the **vertex **of the angle.

In the above image, the angle is called angle AOB or **∠AOB.**

It can also be called angle BOA or **∠**BOA.

The symbol **∠ **represents the word 'angle'.

While naming angle, please remember that **the vertex is always in the centre**.

For example **∠AOB or ∠BOA. O is always is at the centre.**

### Types of Angles

In this section you will learn about different types of angles in geometry. There are four important types of angles - right angle, acute angle, obtuse angle, straight angle

**Right Angle:** A right angle is formed when one of its arm is horizontal and the other is vertical.

Below is an image of a right angle. Carefully see its arms.

A right angle is marked as **∟**.

Let's see some real life example of right angles.

At **3 o' clock**, the hands of a clock form a right angle. See the image given below.

Let's see another example. At **9 o' clock **also the hands of a clock form a right angle. See the image given below.

**Acute Angle:** An acute angle is less than a right angle.

The image given below is an acute angle.

Let's see one example of acute angle.

**Obtuse Angle:** An obtuse angle is greater than a right angle.

Below image is an obtuse angle.

At 5 o' clock, the hands of a clock make an obtuse angle. See the image given below.

**Zero Angle: **When two arms overlap each other, they make an angle that is called zero angle.

For example, at 12 o' clock both hands of a clock overlap each other to make a zero angle.

**Straight Angle:** An angle made by arms going in opposite direction is called a straight angle.

For example, the hands of a clock make a straight angle at **6 o' clock**.

### Closed Figures

Figures that are closed from all sides are called *closed figures*.

Look at the figures given below. They have three or more line segments. Such closed figures are called **polygons**.

Some examples of polygons are triangle, quadrilaterals (rectangle, square).

**Triangle:** It is a polygon with 3 line segments and 3 vertices. It also has 3 angles. The figure given below is a triangle.

The above triangle can be written as △ABC. The symbol △ stands for a triangle.

A triangle (△ABC) has the following properties:

- The line segments are
**AB**,**BC**and**CA**. - The vertices are
**A**,**B**and**C**. - The angles are
**∠A,****∠B and****∠C.**

**Quadrilaterals:** A polygon formed by four line segments is called a quadrilateral.

The four line segments are the four sides of the quadrilateral.

A quadrilateral has 4 sides, 4 vertices and 4 angles. See the image given below.

Examples of quadrilaterals are rectangle and square.

**Rectangle: **A quadrilateral in which opposite sides are equal and all angles are right angles is called a rectangle.

The image given below is an example of a rectangle. Here, **ABCD is a rectangle**.

**Square:** A rectangle in which all sides are equal is a square.

Thus, a square is a quadrilateral in which all sides are equal and all angles are right angles.

See the image given below. Here, **ABCD is a square**.

**Please Note:** A square is a rectangle but a rectangle is not a square