NCERT Solutions for Class 7 maths Chapter 5: Parallel and Intersecting Lines

Solving questions with the help ofGanita Prakash Class 7 Solutionsand Class 7 Maths Chapter 5 Parallel and Intersecting Lines NCERT Solutions Question Answer improves confidence.

NCERT Class 7 Maths Chapter 5 Parallel and Intersecting Lines Solutions Question Answer

Ganita Prakash Class 7 Chapter 5 Solutions Parallel and Intersecting Lines

NCERT Class 7 Maths Ganita Prakash Chapter 5 Parallel and Intersecting Lines Solutions Question Answer

Is this always true for any pair of intersecting lines?
Solution:
Yes. When two lines intersect, they form four angles at a point of intersection. The angles directly opposite each other at this point are called vertically opposite angles, and they are always equal in measure.

Figure it Out (Page 108)

List all the linear pairs and vertically opposite angles you observe from Figure:


Solution:

Are line segments OP and QR likely to meet if they are extended?
Solution:
If two lines are parallel, they will never meet, regardless of how far they are extended. Thus, line segments OP and QR didn’t meet when extended, as they are parallel.

Which pairs of lines appear to be parallel in the Figure below?

Solution:
Two lines are said to be parallel when they do not meet at any point.
Here, lines a, i, and h are parallel to each other;
Line c is parallel to line g;
Line d is parallel to line f;
Line e is parallel to line b.

Figure it Out (Pages 113-114)

Figure it Out (Page 119)

Can you draw a line parallel to l, that goes through point A? How will you do it with the tools from your geometry box? Describe your method.

Solution:
Tools needed: Ruler, Set-squares (right-angled triangle), Pencil

Steps:

Making Parallel Lines through Paper Folding

NCERT In-Text Questions (Page 120)

Let us try to do the same with paper folding.
For a line l (given as a crease), how do we make a line parallel to l such that it passes through point A?
We know how to fold a piece of paper to get a line perpendicular to l.
Now, try to fold a perpendicular to l such that it passes through point A.
Let us call this new crease t.
Now, fold a line perpendicular to t passing through A again.
Let us call this line m.
The lines l and m are parallel to each other.

Why are lines l and m parallel to each other?
Solution:
Line t is perpendicular to line l; line m is also perpendicular to line t. Thus, if two lines are perpendicular to the same line, they are parallel to each other. Thus, lines l and m are parallel to each other because they share the same perpendicular relationship with line t.

Figure it Out (Pages 123-125)

Since alternate angles formed by a transversal intersecting a pair of parallel lines are always equal to each other. Therefore, b = 52°.

The sum of the interior angles on the same side of the transversal always adds up to 180°.
So, 180° – 99° = 81°. Therefore, c = 81°.

The sum of the interior angles on the same side of the transversal always adds up to 180°.
So, 180° – 81° = 99°. Therefore, d = 99°.

Alternate interior angles formed by a transversal intersecting a pair of parallel lines are always equal to each other. Therefore, e = 69°.

The sum of the interior angles on the same side of the transversal always adds up to 180°. So, 180°- 132° = 48°. Therefore, f = 48°.

Corresponding angles formed by a transversal intersecting a pair of parallel lines are always equal to each other. Therefore, g = 122°.

Alternate interior angles formed by a transversal intersecting a pair of parallel lines are always equal to each other. Therefore, h = 15°.

Alternate interior angles formed by a transversal intersecting a pair of parallel lines are always equal to each other. Therefore, i = 54°.

Alternate interior angles formed by a transversal intersecting a pair of parallel lines are always equal to each other. Therefore, j = 97°.

Parallel Illusions

NCERT In-Text Questions (Page 125)

There do not seem to be any parallel lines here. Or, are there?

What causes these illusions?
Solution:
(a) At first glance, this image may appear to be a confusing mix of lines going in all directions, giving the impression that nothing is straight or parallel. However, if we take a closer look, we can see that the vertical lines are perfectly straight, evenly spaced, and are parallel. In contrast, the other lines in the image fan out like spokes on a wheel. These lines are not parallel; they are slanted and converge at a central point. Due to their orientation and the way they intersect with the vertical lines, our brains can become misled. This phenomenon is known as an optical illusion. It occurs because the slanted lines create a sensation that everything is angled or distorted. The focal point in the centre draws our attention and makes it difficult to concentrate on the vertical lines.

(b) This pattern appears to be filled with tilted or zigzagging lines, and the black shapes create a confusing background. However, if we look closely at the white spaces in between, we can see that the horizontal white lines are parallel. So why do they not seem that way? The bold, slanted black shapes visually interrupt the lines, causing our eyes to perceive them as slanting or shifting. This phenomenon is known as an optical illusion—our brain interprets the shapes around the lines, leading us to see something that isn’t there.

(c) When you first look at this picture, it appears that nothing is parallel. The lines seem bent, the shape appears to curve inward, and everything feels like it’s being pulled toward the centre. However, the two horizontal lines at the top and bottom of the image are parallel! This is a classic optical illusion. It occurs because of the many diagonal lines radiating from a central point, resembling the spokes of a wheel. These radiating lines distort our perception, leading our brains to interpret the space as curved due to the way the lines fan out from the centre, creating a sense of depth. As a result, the ends of the horizontal lines seem to bend, even though they are perfectly straight. This visual trick deceives our eyes into believing that the horizontal lines are curving inward, but if we measure them or place a ruler along them, we can see that they are straight and parallel.