In Fig.6.6, which of the two lines are parallel and why
Solution:
The figure (1) represents two lines l and m cut by a transversal n.
We have to determine if the lines are parallel or not.
We know that if a transversal cuts two parallel lines, then the sum of the interior angles lying on the same side of the transversal is supplementary.
From the figure,
The interior angles on the same side of the transversal are 132° and 48°
Now, sum of interior angles = 132° + 48°
= 180°
Therefore, the lines l and m are parallel.
The figure (2) represents two lines p and q cut by a transversal r.
We have to determine if the lines are parallel or not.
We know that if a transversal cuts two parallel lines, then the sum of the interior angles lying on the same side of the transversal is supplementary.
From the figure,
The interior angles on the same side of the transversal are 73° and 106°
Now, sum of interior angles = 73° + 106°
= 179°
Sum of interior angles is not equal to 180 degrees.
Therefore, the lines p and q are not parallel.
✦ Try This: Can two obtuse angles be complementary to each other?
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6
NCERT Exemplar Class 9 Maths Exercise 6.2 Problem 9
In Fig.6.6, which of the two lines are parallel and why
Summary:
Two or more lines that lie in the same plane and never intersect each other are known as parallel lines. They are equidistant from each other and have the same slope. In fig 6.6 the lines l and m are parallel as the sum of interior angles is equal to 180 degrees in figure 1 and not parallel in figure 2 as the sum is less than 180 degrees
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