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 $\overline{A B}$ .

3.0Line

It has no end points. It is denoted by $A B$ .

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 $AP$ .

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:

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

For example, if two rays $O A$ and $OB$ meet at point O, the angle is represented as $∠ A OB$ .

Types of Angles

Angles are classified based on their measurement:

Acute Angle: An acute angle measures less than $9 0^{\circ}$ . These angles are small and sharp. It is always smaller than a right angle.

Example: $4 5^{\circ}, 6 0^{\circ}$ .
Real-life Example: The hands of a clock at 10:10.

Right Angle: A right angle is an angle that measures exactly $9 0^{\circ}$ . 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.

Obtuse Angle: An obtuse angle measures more than $9 0^{\circ}$ but less than $18 0^{\circ}$ . These angles are broad and open. This is the angle formed when two opposite rays meet at a point.

Example: $12 0^{\circ}, 15 0^{\circ}$ .
Real-life Example: The angle of an open door when it’s slightly ajar.

Straight Angle: A straight angle measures exactly $18 0^{\circ}$ . 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.

Reflex Angle: A reflex angle measures more than $18 0^{\circ}$ but less than $36 0^{\circ}$ . These angles are very large and wrap around a significant part of a circle.

Example: $27 0^{\circ} .$
Real-life Example: The hands of a clock at 10:10 (taking the outer part of the angle).

Complete Angle: A complete angle measures exactly $36 0^{\circ}$ . 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 $18 0^{\circ}$ (in a semi-circular protractor) or $0^{\circ}$ to $36 0^{\circ}$ (in a circular protractor).

Parts of a Protractor:

Baseline: The straight edge of the protractor used to align with one arm of the angle.
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.
Degree Markings: The curved edge is marked with degrees from $0^{\circ}$ to $18 0^{\circ}$ (or $0^{\circ}$ to $36 0^{\circ}$ in a circular protractor).
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 centre 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 centre 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.

7.0Benefits of CBSE Notes for Class 6 Maths Chapter 2 - Lines and Angles

Focus on Key Points: CBSE Notes for Class 6 highlight the most crucial information and formulas, ensuring that students don't miss out on essential details.
Easy Accessibility: Digital notes can be accessed anytime and anywhere, making learning more convenient.
Self-Paced Learning: Students can refer to the CBSE Notes at their own pace, revisiting topics they find challenging.
Reduced Textbook Burden: Notes can act as a handy reference, reducing the need to constantly flip through the entire NCERT Solutions textbook.
Preparation for Higher Classes: A strong foundation in the concepts of lines and angles in CBSE Class 6 is crucial for understanding more advanced geometry in higher classes.