CBSE Notes Class 6 Maths Chapter 2 Lines and Angles

In Chapter 2 of CBSE Class 6 Maths, we explore the concepts of Points, Line Segments, and Rays. A Line Segment is a part of a line with two endpoints, while a Ray has one fixed endpoint and extends infinitely in one direction. Angles are formed when two rays meet at a point. We study Types of Angles such as acute, right, obtuse, and reflex. The Degree is used to measure angles, and a Protractor is a tool used to measure angles accurately.

1.0Points

A point determines a precise location, but it has no height.

Ex: Point A, Point B, Point C, etc

2.0Line Segments

It has two end points. It is denoted by either  . The points A and B are called the end points of the line segment $\overline{AB}$.

3.0Line

It has no end points. It is denoted by $\overleftrightarrow{AB}$.

4.0Ray

A ray is a portion of a line that starts at one point (called the starting Point or initial point) and goes on endlessly in a direction.

It is denoted as $\overrightarrow{\mathrm{AP}}$.

5.0Angle

An angle is formed when 2 rays meet at a common endpoint called the vertex. Angles are measured in degrees (${}^{\circ }$).

Parts of an Angle:

1. Arms: The two rays that form the angle.
2. Vertex: The common endpoint of the 2 rays.

For example, if two rays $\overrightarrow{OA}$ and $\overrightarrow{OB}$ meet at point O, the angle is represented as $\angle AOB$.

Types of Angles

Angles are classified based on their measurement:

1. Acute Angle: An acute angle measures less than $90^{\circ }$. These angles are small and sharp. It is always smaller than a right angle.

• Example: $45^{\circ },60^{\circ }$.
• Real-life Example: The hands of a clock at 10:10.

2. Right Angle: A right angle is an angle that measures exactly $90^{\circ }$. It forms a perfect "L" shape. It is the baseline for measuring other types of angles.

• Example: The corner of a square or rectangle.
• Real-life Example: The corner of a notebook, book, or a square, The edge of a table.

3. Obtuse Angle: An obtuse angle measures more than $90^{\circ }$ but less than $180^{\circ }$. These angles are broad and open. This is the angle formed when two opposite rays meet at a point.

• Example: $120^{\circ },150^{\circ }$.
• Real-life Example: The angle of an open door when it’s slightly ajar.

4. Straight Angle: A straight angle measures exactly $180^{\circ }$. It looks like a straight line. It is equal to two right angles.

• Example: A straight line.
• Real-life Example: The angle formed by the hands of a clock at 6:00. A flat bridge or the horizon.

5. Reflex Angle: A reflex angle measures more than $180^{\circ }$ but less than $360^{\circ }$. These angles are very large and wrap around a significant part of a circle.

• Example: $270^{\circ }.$
• Real-life Example: The hands of a clock at 10:10 (taking the outer part of the angle).

6. Complete Angle: A complete angle measures exactly $360^{\circ }$. It represents one full rotation or revolution. It forms a perfect circle.

• Example: A full circle.
• Real-life Example: The wheels of a car rotating one full turn, A merry-go-round making one complete spin.

6.0Degree and Protractor

Degree measures of angles can be measured using a protractor.

A protractor is a tool used to measure and draw angles. It is semi-circular or circular in shape and marked with degree measurements, ranging from $0^{\circ }$ to $180^{\circ }$ (in a semi-circular protractor) or $0^{\circ }$ to $360^{\circ }$ (in a circular protractor).

Parts of a Protractor:

1. Baseline: The straight edge of the protractor used to align with one arm of the angle.
2. Center or Origin: The midpoint at the base of the protractor, marked with a small hole or dot. This is where the vertex of the angle is placed.
3. Degree Markings: The curved edge is marked with degrees from $0^{\circ }$ to $180^{\circ }$ (or $0^{\circ }$ to $360^{\circ }$ in a circular protractor).
4. Inner and Outer Scales:

• The inner scale is used to measure angles starting from the right (clockwise).
• The outer scale is used to measure angles starting from the left (counter-clockwise).

How to Use a Protractor to Measure an Angle

Step 1: Place the Protractor

• Align the baseline of the protractor with one arm of the angle.
• Place the center of the protractor at the vertex of the angle.

Step 2: Read the Degree Markings

• Locate the other arm of the angle on the protractor scale.
• Check which degree marking it passes through. Use the correct scale (inner or outer) based on the angle's orientation.

Step 3: Note the Measurement

• Record the degree where the arm crosses the protractor scale. This is the angle’s measure.

Steps to Draw an Angle Using a Protractor:

Step 1: Draw a Baseline

• Use a ruler to draw a straight line. This will act as one arm of the angle.

Step 2: Place the Protractor

• Align the baseline of the protractor with the line you just drew, and place the center at one end of the line.

Step 3: Mark the Angle

• Locate the desired angle measure on the protractor scale and make a small dot at that degree.

Step 4: Draw the Second Arm

• Take away the protractor and use a ruler to connect the dot with the vertex of the angle. This forms the second arm.