Acute Angle: An angle that measures between 0° and 90° is called an acute angle. Obtuse angle: An angle that measures between 90° and 180° is called an obtuse angle. Right angle: An angle that is equal to 90° is called a right angle. Reflex angle: An angle greater than 180° but less than 360° is called a reflex angle.
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Sure, here are some notes for the math lesson "Lines and Angles" for class 9th:
1. Line:
- A line is a straight path that extends infinitely in both directions.
- It has no thickness and is represented by a straight line with two arrowheads.
- It is denoted by a small letter placed on top of two points on the line (e.g., line AB is denoted as AB).
2. Types of Angles:
- Acute Angle: An angle with a measure between 0 and 90 degrees.
- Right Angle: An angle with a measure of exactly 90 degrees.
- Obtuse Angle: An angle with a measure between 90 and 180 degrees.
- Straight Angle: An angle with a measure of exactly 180 degrees.
- Reflex Angle: An angle with a measure between 180 and 360 degrees.
3. Types of Lines:
- Intersecting Lines: Lines that cross each other at a single point.
- Parallel Lines: Lines that never intersect and remain at the same distance apart.
- Perpendicular Lines: Lines that intersect at a right angle (90 degrees).
- Transversal: A line that intersects two or more lines at distinct points.
4. Pair of Angles Formed by Transversal:
- Corresponding Angles: Angles located at the same position on the opposite sides of the transversal when two parallel lines are intersected by a transversal.
- Alternate Interior Angles: Angles located between the two lines on the opposite sides of the transversal when two parallel lines are intersected by a transversal.
- Alternate Exterior Angles: Angles located outside the two lines on the opposite sides of the transversal when two parallel lines are intersected by a transversal.
- Consecutive Interior Angles: Pairs of angles on the same side of the transversal and inside the two lines.
5. Properties of Parallel Lines:
- Corresponding Angles are equal.
- Alternate Interior Angles are equal.
- Alternate Exterior Angles are equal.
- Consecutive Interior Angles are supplementary (their sum is 180 degrees).
6. Angle Sum Property of a Triangle:
- The sum of the interior angles of a triangle is always 180 degrees.
7. Angle Sum Property of a Quadrilateral:
- The sum of the interior angles of a quadrilateral is always 360 degrees.
8. Co-Interior Angles Property:
- When two parallel lines are intersected by a transversal, the co-interior angles add up to 180 degrees.
Remember to illustrate the concepts with diagrams and examples to aid understanding. These notes should provide a good foundation for the "Lines and Angles" lesson in class 9th mathematics.
Answers & Comments
Step-by-step explanation:
Acute Angle: An angle that measures between 0° and 90° is called an acute angle. Obtuse angle: An angle that measures between 90° and 180° is called an obtuse angle. Right angle: An angle that is equal to 90° is called a right angle. Reflex angle: An angle greater than 180° but less than 360° is called a reflex angle.
hope it will help you dear please mark my answer as brain list✨
Verified answer
Answer:
Sure, here are some notes for the math lesson "Lines and Angles" for class 9th:
1. Line:
- A line is a straight path that extends infinitely in both directions.
- It has no thickness and is represented by a straight line with two arrowheads.
- It is denoted by a small letter placed on top of two points on the line (e.g., line AB is denoted as AB).
2. Types of Angles:
- Acute Angle: An angle with a measure between 0 and 90 degrees.
- Right Angle: An angle with a measure of exactly 90 degrees.
- Obtuse Angle: An angle with a measure between 90 and 180 degrees.
- Straight Angle: An angle with a measure of exactly 180 degrees.
- Reflex Angle: An angle with a measure between 180 and 360 degrees.
3. Types of Lines:
- Intersecting Lines: Lines that cross each other at a single point.
- Parallel Lines: Lines that never intersect and remain at the same distance apart.
- Perpendicular Lines: Lines that intersect at a right angle (90 degrees).
- Transversal: A line that intersects two or more lines at distinct points.
4. Pair of Angles Formed by Transversal:
- Corresponding Angles: Angles located at the same position on the opposite sides of the transversal when two parallel lines are intersected by a transversal.
- Alternate Interior Angles: Angles located between the two lines on the opposite sides of the transversal when two parallel lines are intersected by a transversal.
- Alternate Exterior Angles: Angles located outside the two lines on the opposite sides of the transversal when two parallel lines are intersected by a transversal.
- Consecutive Interior Angles: Pairs of angles on the same side of the transversal and inside the two lines.
5. Properties of Parallel Lines:
- Corresponding Angles are equal.
- Alternate Interior Angles are equal.
- Alternate Exterior Angles are equal.
- Consecutive Interior Angles are supplementary (their sum is 180 degrees).
6. Angle Sum Property of a Triangle:
- The sum of the interior angles of a triangle is always 180 degrees.
7. Angle Sum Property of a Quadrilateral:
- The sum of the interior angles of a quadrilateral is always 360 degrees.
8. Co-Interior Angles Property:
- When two parallel lines are intersected by a transversal, the co-interior angles add up to 180 degrees.
Remember to illustrate the concepts with diagrams and examples to aid understanding. These notes should provide a good foundation for the "Lines and Angles" lesson in class 9th mathematics.