ALLEN Coaching
ApplyRegister for ALLEN Scholarship Test & get up to 90% Scholarship
Parallel lines are lines that are equidistant from each other. Parallel lines never intersect or meet each other at any point. A transversal line intersects two or more lines at distinct points. As shown in the figure, line l crosses lines m and n at P and Q, respectively. Line l is thus a transversal for lines m and n.
In this figure,
Consecutive interior angles, also known as associated angles or co-interior angles, are interior angles on the same side of the transversal. The corresponding angles are identical when a transversal connects two parallel lines. The two lines are parallel if a transversal intersects them so that a pair of corresponding angles are equal.
NCERT Solutions Class 9 Maths exercise 6.2 – this exercise includes some very important theorems from the examination point of view. So, the theorems and their proof given in the NCERT Books are:
Q1. In Fig. 6.23, if AB
Solution:
Given that,
AB || CD and CD || EF and
Therefore, AB || EF and
Again, CD || AB
As the angles on the same side of a transversal sum is 180°
Putting the value of
Then
By equation (i), we get the value of
Q2. In Fig. 6.24, if AB
Solution:
Given,
AB || CD, EF
In the above figure,
GE is transversal. So, that
Also,
Since AB is a straight line
Therefore,
So,
Solution:
Draw a line EF parallel to the ST through R.
Since PQ || ST and ST || EF
Again,
Thus,
Q4. In Fig. 6.26, if AB
Solution:
Given,
AB || CD,
PQ is a transversal. So,
Again, PR is a transversal. So,
Solution:
Draw a ray BL
So, BL || CM and BC is a transversal
It is known that, angle of incidence = the angle of reflection
So,
Adding eq (i) and eq (ii), we get
Both the interior angles are equal
Hence AB || CD
Also Read
Lines and Angles Exercise 6.1
The following key concepts are covered in this exercise:
1. Corresponding angles - Angles that are on the same side and corresponding position of the traversal.
2. Alternate interior angles - Angles that are between two parallel lines and on opposite sides of the transversal.
3. Alternate exterior angles - Angles that are on the outside of the two parallel lines and opposite sides of the transversal.
4. Consecutive interior angles - Angles that are on the same side of the transversal and between the two parallel lines.
5. Lines parallel to the same line - If two lines are parallel to the same line, then these two lines are parallel to each other also.
Also See
Students must check the NCERT solutions for Class 9 Maths and Science given below:
Students must check the NCERT exemplar solutions for Class 9 Maths and Science given below:
This exercise is about Parallel Lines and a Transversal, types of angles like vertically opposite angles and axioms that are formed due to this intersection.
Parallel lines are coplanar straight lines that never intersect with each other at any point.
Consecutive angles are the angles formed by a transversal that intersects two parallel lines. Each angle forms a pair of consecutive angles which lies on each of the parallel lines on any one side of the transversal which can be either be interior or exterior.
Four angles are formed on each of the parallel lines. Thus, making the total sum eight.
Admit Card Date:17 April,2025 - 17 May,2025
Exam Date:01 May,2025 - 08 May,2025
Register for ALLEN Scholarship Test & get up to 90% Scholarship
Get up to 90% Scholarship on Offline NEET/JEE coaching from top Institutes
This ebook serves as a valuable study guide for NEET 2025 exam.
This e-book offers NEET PYQ and serves as an indispensable NEET study material.
As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters