NCERT Solutions for Class 9 Maths Chapter 6 – Lines And Angles
In NCERT Solutions for Class 9 Maths Chapter 6 ‘Lines and Angles’, you will learn about the basic yet most important definitions of geometry. The main concepts of Chapter 6 include Pairs of Angles, Linear Pair Axioms, Parallel Lines and Transversal, Lines Parallel to Same Line and Angle Sum Property of A Triangle. This Chapter has 3 sets of exercises with a total of 18 questions.
Maths NCERT Solutions for Class 9 Chapter 6 will aid you in understanding the applications of lines and angles in various concepts of physics such as drawing ray diagrams and also in other instances of practical life. You will also recall the basic terms and definitions in this Chapter such as line segment, collinear and noncollinear points, angle, arms of an angle, reflex angles, supplementary angles, vertically opposite angles, etc.
By practising NCERT Maths Class 9 Chapter 6 examples, you will be able to memorize the theorems and definitions easily. Lines and Angles is a conceptual chapter that, if understood, will help you in other chapters of Geometry as well. Our Solutions for CBSE NCERT Class 9 Maths Chapter 6 will guide you at every point. Refer to the Summary of Chapter 6 given below so that you can solve all the questions quickly.
Quick Glance at the Key Points in NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles
Essential Terms and Definitions
- A line segment is a part of the line with two ends and is terminating in nature.
- A ray has one endpoint whereas its other end extends indefinitely.
- Collinear points: If on the same line, lies the given three points, then they are known as collinear points; else they are known as non-collinear points.
- Angle: An angle is formed where the terminating ends of two rays meet. Their point of intersection is called the vertex of the angle and the rays are termed the arms of the angle.
- An acute angle measures between 0° and 90°, a right angle measures exactly 90° and an obtuse angle measures greater than 90° but less than 180°. A reflex angle is greater than 180° but less than 360°.
- Complementary angles are the pair of angles whose sum is 90° whereas supplementary angles are the pair of angles whose sum is 180°
- There are 3 conditions for two angles to be adjacent: they should have a common aim and a common vertex and the uncommon arms should not be on the same side of the common arms.
- Linear pair is formed when the uncommon arms make up a straight line such that their sum is 180°
Parallel lines are known as non-intersecting lines and the length of the perpendicular from corresponding points between such lines is equal. This length is known as the distance between parallel lines.
Axiom 1: If we draw a ray beginning from a line, it will form two adjacent angles whose sum is equal to 180°. Therefore, these are supplementary angles with respect to one another.
Axiom 2: If we find that the sum of any two adjacent angles is 180°, then the uncommon arms on both sides of the common arms together form a straight line.
Axiom 3: According to the corresponding angles axiom, all the pairs of corresponding angles are equal when a transversal intersects two parallel lines.
Axiom 4: If a transversal intersects a pair of lines and the corresponding angles so formed are found to be equal, then it is a pair of parallel lines.
Key highlights of CBSE NCERT Class 9 Maths Chapter 6
- Both the pairs of vertically opposite angles are equal in the event of the intersection of two lines.
- All pairs of alternate interior angles are equal when a transversal intersects two parallel theorems. This can be proved with the help of the corresponding angle axiom
- If a transversal intersects a pair of lines and the alternate angles so formed are found to be equal, then the pair constitutes parallel lines.
- All pairs of co-interior angles are supplementary in the event of the intersection of two parallel lines by a transversal.
- If a transversal intersects a pair of lines and the co-interior angles so formed are supplementary to one another, then the two lines are parallel.
- Two lines that happen to be parallel to the same line are parallel to one another.
- The sum total of all the angles in a triangle is 180°. This is also known as the angle sum property of a triangle.
- The exterior angle in a triangle, if one of its sides is extended outwards is the
Exercise Wise Discussion of NCERT Solutions for Class 9 Maths Chapter 6
- The NCERT Solutions for Class 9 Maths Chapter 6 Exercise 6.1 will help you identify different types of angles in the figures and calculate the value of angles in different problems. Figures are attached alongside the question to make it convenient to understand the hypothesis.
- Chapter 6 Exercise 6.2 is more advanced in terms of difficulty levels and will employ the application of all theorems learned in this chapter. The Instasolv team of subject matter experts has prepared a step by step solutions and self-study material for you.
- Exercise 6.3 for Chapter 6 is an interesting one. It requires you to revise both the theorems given with respect to the properties of triangles.
NCERT Solutions Class 9 Maths Chapter 6 by Instasolv
- The NCERT Solutions for Class 9 Maths Chapter 6 are a one-stop destination for all your doubts in this Chapter.
- You can rely on our NCERT Solutions for better marks in Maths. Each and every question of the NCERT book is covered with in-depth answers.
- Our subject matter experts are well-versed with the CBSE Class 9 Maths Syllabus and exam pattern which reflects in our NCERT Solutions.