Question 1

Draw some lines perpendicular to the lines given on the dot paper in the Figure.

Accepted Answer

Do it yourself.

Source: This question is from Parallel and Intersecting Lines, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Parallel and Intersecting Lines: Lines, Perpendicular, Dot, Paper, Figure, Parallel and Intersecting Lines. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Parallel and Intersecting LinesQ2: In the given figure, mark the parallel lines using the notation given above (single arrow, double...
Q3: In the dot paper following, draw different sets of parallel lines. The line segments can be of...
Q4: Using your sense of how parallel lines look, try to draw lines parallel to the line segments on...
Q5: In the figure, which line is parallel to line a—line b or line c? How do you decide this?
Q6: What is the measure of angle ∠NOP in the given figure? [Hint: Draw lines parallel to LM and PQ...
Practice more questions from Parallel and Intersecting Lines &mdash; Mathematics, Class 7 CBSE

Question 2

In the given figure, mark the parallel lines using the notation given above (single arrow, double arrow, etc). Mark the angle between perpendicular lines with a square symbol.
(a) How did you spot the perpendicular lines?
(b) How did you spot the parallel lines?

Accepted Answer

(a) To spot perpendicular lines in a geometric figure, observe if lines intersect at a 90° angle.
(b) To spot parallel lines in a geometric figure, observe if lines never intersect at any point.

Question 3

In the dot paper following, draw different sets of parallel lines. The line segments can be of different lengths but should have dots as endpoints.

Accepted Answer

Do it Yourself.

Source: This question is from Parallel and Intersecting Lines, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Parallel and Intersecting Lines: Dot, Paper, Sets, Parallel, Lines, Line. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Parallel and Intersecting LinesQ2: In the given figure, mark the parallel lines using the notation given above (single arrow, double...
Q4: Using your sense of how parallel lines look, try to draw lines parallel to the line segments on...
Q5: In the figure, which line is parallel to line a—line b or line c? How do you decide this?
Q6: What is the measure of angle ∠NOP in the given figure? [Hint: Draw lines parallel to LM and PQ...
Practice more questions from Parallel and Intersecting Lines &mdash; Mathematics, Class 7 CBSE

Question 4

Using your sense of how parallel lines look, try to draw lines parallel to the line segments on this dot paper.
(a) Did you find it challenging to draw some of them?
(b) Which ones?
(c) How did you do it?

Accepted Answer

(a) – (c) Do it yourself

Source: This question is from Parallel and Intersecting Lines, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Parallel and Intersecting Lines: Sense, Parallel, Lines, Look, Try, Line. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Parallel and Intersecting LinesQ2: In the given figure, mark the parallel lines using the notation given above (single arrow, double...
Q3: In the dot paper following, draw different sets of parallel lines. The line segments can be of...
Q5: In the figure, which line is parallel to line a—line b or line c? How do you decide this?
Q6: What is the measure of angle ∠NOP in the given figure? [Hint: Draw lines parallel to LM and PQ...
Practice more questions from Parallel and Intersecting Lines &mdash; Mathematics, Class 7 CBSE

Question 5

In the figure, which line is parallel to line a—line b or line c? How do you decide this?

Accepted Answer

In the given figure, line a is parallel to line c because these two lines are always the same distance apart and never meet, no matter how far they go.
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:
Place the set square so that one side is along the line l.
Hold the ruler against the other side of the set square (the ruler won’t move).
Slide the set square along the ruler until one side reaches point A.
Draw a line along the edge of the set square through point A.
This new line is parallel to line l and passes through point A.
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)

Question 6

What is the measure of angle ∠NOP in the given figure?
[Hint: Draw lines parallel to LM and PQ through points N and O]

Accepted Answer

Draw a line RS through N, which is parallel to line LM, and line TU through O, which is parallel to line PQ.
∠LMN = ∠MNS [Alternate Angles]
Therefore, w° = 56°
Given, ∠MNO = 96°
w° + x° = 96°
x° = 96° – 40° = 56°
Now, RS is parallel to TU, and NO is a transversal.
So, ∠SNO = ∠NOT [Alternate Angles]
Therefore, y° = x° = 56°
Now TU is parallel to PQ, and OP is a transversal.
So, ∠TOP = ∠OPQ [Alternate Angles]
z° = 52° [Given ∠OPQ = 52°]
Thus, a° = y° + z° = 56° + 52° = 108°
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.