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Important Formulas: Lines and Angles | Mathematics for Class 6 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°
Question for Important Formulas: Lines and Angles
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FAQs on Important Formulas: Lines and Angles - Mathematics for Class 6
| 1. What are the different types of angles formed when a transversal crosses two parallel lines? |  |
| 2. How can we identify if two lines are perpendicular to each other? | |
Ans. Two lines are perpendicular to each other if the angle formed between them is a right angle, which measures 90 degrees.
| 3. What is the sum of the interior angles of a triangle? | |
Ans. The sum of the interior angles of a triangle is always 180 degrees.
| 4. How do you calculate the measure of an exterior angle of a triangle? | |
Ans. The measure of an exterior angle of a triangle is equal to the sum of the two remote interior angles.
| 5. How can we determine if two lines are parallel by looking at their slopes? | |
Ans. Two lines are parallel if their slopes are equal. If the slopes of two lines are equal, then the lines are parallel to each other.
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