Important Formulas: Lines and Angles | Maths for Class 6 (Ganita Prakash) - New NCERT PDF Download

1. Point: A point is a precise location with no size—no length, width, or height. It is represented by a small dot. Points are labeled with capital letters, like  A, B, or C.

2. Line Segment: A line segment has two distinct endpoints and is the shortest distance between these points.

3. Line: A line extends infinitely in both directions and has no endpoints.

4. Ray: A ray starts at one specific point and extends infinitely in one direction.

5. Angle: An angle is formed by two rays sharing a common starting point, known as the vertex. The rays are called the arms of the angle. Angles are named using points on each arm and the vertex, like  ∠AOB, with the vertex in the middle.

6. Comparing Angles:

• Superimposition: Overlaying one angle on top of another to compare their sizes.
• Alternative Method: Using a transparent circle to compare angles without superimposition.

7. Types of Angles:

• Right Angle: Exactly 90°, like the corner of a piece of paper.
• Straight Angle: Exactly 180°, forming a straight line.
• Acute Angle: Less than 90°, like a barely open book.
• Obtuse Angle: More than 90° but less than 180°, like a door opened wider than a right angle.

8. Measuring Angles:

• Degrees: A full circle has 360°, a straight angle is 180°, and a right angle is 90°.
• Protractor: Tool for measuring angles, with units marked in degrees.
• Labeled Protractor: Displays numbers for easy measurement.
• Unlabeled Protractor: Requires counting marks.

9. Angle Bisector: A line that divides an angle into two equal parts.

10. Common Mistakes with Protractors:

• Incorrect Placement: Ensure the center is on the vertex.
• Misalignment: Align one arm of the angle with the 0° line.
• Wrong Scale: Use the correct scale based on the protractor’s alignment.

11. Drawing Angles:

Example: To draw a 40° angle, use a protractor to measure and mark the angle, then draw the second arm.

12. Types of Angles and Their Measures:

• Straight Angle: 180°
• Right Angle: 90°
• Acute Angle: More than 0° and less than 90°
• Obtuse Angle: More than 90° and less than 180°
• Reflex Angle: More than 180° and less than 360°