NCERT Solutions for Class 7 Maths Chapter 7 a Tale of Three Intersecting Lines (PDF) – 2026-27

NCERT Solutions for Class 7 Maths Chapter 7 a Tale of Three Intersecting Lines provide clear, step-by-step answers to every exercise and in-text question from the chapter a Tale of Three Intersecting Lines of the NCERT textbook Ganita Prakash. Prepared by subject experts as per the latest NCERT (CBSE) syllabus for 2026-27, these NCERT Solutions for Class 7 Maths help you understand each concept, write exam-ready answers, and check your own solutions. You can read them online below or download the free Class 7 Maths Chapter 7 question-answer PDF.

NCERT Solutions for Class 7 Maths Chapter 7 a Tale of Three Intersecting Lines

• Class: Class 7
• Subject: Maths
• Chapter: Chapter 7 – a Tale of Three Intersecting Lines
• Textbook: Ganita Prakash (NCERT)
• Study material: NCERT Solutions – questions with answers, free PDF

These solutions answer all the exercise questions of Chapter 7 a Tale of Three Intersecting Lines — including the in-text questions, short-answer and long-answer questions, and activities — with complete explanations so you can follow the method, not just the final answer. Read the full solutions below.

NCERT Solutions Class 7 Maths Chapter 7 a Tale of Three Intersecting Lines View Download

NCERT Solutions for Class 7 Maths Chapter 7 PDF Download

You can read the NCERT Solutions for Class 7 Maths Chapter 7 online above, or download the complete question-answer PDF to study a Tale of Three Intersecting Lines offline at any time.

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NCERT Solutions for Class 7 Maths Chapter 7 PDF Download Link – Click Here to Download Solutions PDF

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Questions Covered in This Chapter

These NCERT Solutions answer all 75 questions of this chapter. The questions solved are:

1. What happens when the three vertices lie on a straight line?
2. Construct a triangle in which all the sides are of length 4 cm.
3. How did you construct this triangle and what tools did you use? Can this construction be done only using a marked ruler (and a pencil)?
4. How do we make this construction more efficient?
5. Let C be the point of intersection of the arcs. The construction ensures that both AC and BC are of length 4 cm. Can you see why?
6. How do we construct triangles that are not equilateral?
7. Construct a triangle of sidelength 4 cm, 5 cm and 6 cm.
8. How do we construct this triangle more efficiently?
9. Construct triangles having the following sidelengths (all the units are in cm): (a) 4, 4, 6 (b) 3, 4, 5 (c) 1, 5, 5 (d) 4, 6, 8 (e) 3.5, 3.5, 3.5
10. Use the points on the circle and/or the centre to form isosceles triangles.
11. Use the points on the circles and/or their centres to form isosceles and equilateral triangles. The circles are of the same size.
12. Construct a triangle with sidelengths 3 cm, 4 cm, and 8 cm. What is happening? Are you able to construct the triangle?
13. Here is another set of lengths: 2 cm, 3 cm, and 6 cm. Check if a triangle is possible for these sidelengths.
14. Try to find more sets of lengths for which a triangle construction is impossible. See if you can find any pattern in them.
15. Consider the lengths 10 cm, 15 cm and 30 cm. Does there exist a triangle having these as sidelengths?
16. Imagine you are at the entrance of the tent and want to go to the tree. Which is the shorter path: (i) the straight-line path to the tree (the red path) or (ii) the straight-line path from the tent to the pole, followed by the straight-line path from the pole to the tree (the yellow path)?
17. Can this understanding be used to tell something about the existence of a triangle having sidelengths 10 cm, 15 cm and 30 cm?
18. Can we say anything about the existence of a triangle having sidelengths 3 cm, 3 cm and 7 cm? Verify your answer by construction.
19. “In the rough diagram in Fig. 7.4, is it possible to assign lengths in a different order such that the direct paths are always coming out to be shorter than the roundabout paths? If this is possible, then a triangle might exist.” Is such rearrangement of lengths possible in the triangle?
20. We checked by construction that there are no triangles having sidelengths 3 cm, 4 cm and 8 cm; and 2 cm, 3 cm and 6 cm. Check if you could have found this without trying to construct the triangle.
21. Can we say anything about the existence of a triangle for each of the following sets of lengths? (a) 10 km, 10 km and 25 km (b) 5 mm, 10 mm and 20 mm (c) 12 cm, 20 cm and 40 cm
22. For each set of lengths seen so far, you might have noticed that in at least two of the comparisons, the direct length was less than the sum of the other two (if not, check again!). For example, for the set of lengths 10 cm, 15 cm and 30 cm, there are two comparisons where this happens: 10 < 15 + 30 and 15 < 10 + 30. But this doesn’t happen for the third length: 30 > 10 + 15. Will this always happen? That is, for any set of lengths, will there be at least two comparisons where the direct length is less than the sum of the other two? Explore for different sets of lengths.
23. Further, for a given set of lengths, is it possible to identify which lengths will immediately be less than the sum of the other two, without calculations? [Hint: Consider the direct lengths in the increasing order.]
24. Given three sidelengths, what do we need to compare to check for the existence of a triangle?
25. Does a triangle exist with sidelengths 4 cm, 5 cm and 8 cm? This satisfies the triangle inequality: 8 < 4 + 5 = 9. Why do we not need to check the other two sides?
26. Now, suppose that a circle of radius 5 cm is constructed, centred at B. Can you draw a rough diagram of the resulting figure?
27. Note that in the figure below, AX = 4 cm and AB = 8 cm. So, what is BX? Does this length help in visualising the resulting figure?
28. Which of the following lengths can be the sidelengths of a triangle? Explain your answers. Note that for each set, the three lengths have the same unit of measure. (a) 2, 2, 5 (b) 3, 4, 6 (c) 2, 4, 8 (d) 5, 5, 8 (e) 10, 20, 25 (f) 10, 20, 35 (g) 24, 26, 28
29. Will triangles always exist when a set of lengths satisfies the triangle inequality? How can we be sure?
30. Case 2: Circles do not intersect internally. For this case to happen, what should be the relation between the radii and AB?
31. Can we use this analysis to tell if a triangle exists when the lengths satisfy the triangle inequality?
32. How will the two circles turn out for a set of lengths that do not satisfy the triangle inequality? Find 3 examples of sets of lengths for which the circles: (a) touch each other at a point, (b) do not intersect.
33. Frame a complete procedure that can be used to check the existence of a triangle.
34. Check if a triangle exists for each of the following set of lengths: (a) 1, 100, 100 (b) 3, 6, 9 (c) 1, 1, 5 (d) 5, 10, 12
35. Does there exist an equilateral triangle with sides 50, 50, 50? In general, does there exist an equilateral triangle of any sidelength? Justify your answer.
36. For each of the following, give at least 5 possible values for the third length so there exists a triangle having these as sidelengths (decimal values could also be chosen): (a) 1, 100 (b) 5, 5 (c) 3, 7
37. See if you can describe all possible lengths of the third side in each case, so that a triangle exists with those sidelengths. For example, in case (a), all numbers strictly between 99 and 101 would be possible.
38. How do we construct a triangle if two sides and the angle included between them are given?
39. Construct a triangle ABC with AB = 5 cm, AC = 4 cm and ∠A = 45°.
40. Construct triangles for the following measurements where the angle is included between the sides: (a) 3 cm, 75°, 7 cm (b) 6 cm, 25°, 3 cm (c) 3 cm, 120°, 8 cm
41. We have seen that triangles do not exist for all sets of sidelengths. Is there a combination of measurements in the case of two sides and the included angle where a triangle is not possible? Justify your answer using what you observe during construction.
42. Construct a triangle ABC where AB = 5 cm, ∠A = 45° and ∠B = 80°.
43. Construct triangles for the following measurements: (a) 75°, 5 cm, 75° (b) 25°, 3 cm, 60° (c) 120°, 6 cm, 30°
44. Do triangles exist for every combination of two angles and their included side? Explore.
45. Find examples of measurements of two angles with the included side where a triangle is not possible.
46. Now we make one of the base angles an acute angle, say 40°. What are the possible values that the other angle should take so that the lines don’t meet? (a) Try to find a possible ∠B (marked in the figure) for this to happen. (b) What could be smallest value of ∠B for the lines to not meet?
47. Can you tell the actual value of ∠B be in this case? [Hint: Note that AB is the transversal.]
48. So, for what values of ∠B, does a triangle not exist? Does the length AB play any part here?
49. For each of the following angles, find another angle for which a triangle is (a) possible, (b) not possible. Find at least two different angles for each category: (a) 30° (b) 70° (c) 54° (d) 144°
50. Determine which of the following pairs can be the angles of a triangle and which cannot: (a) 35°, 150° (b) 70°, 30° (c) 90°, 85° (d) 50°, 150°
51. Like the triangle inequality, can you form a rule that describes the two angles for which a triangle is possible? Can the sum of the two angles be used for framing this rule?
52. Let us take two angles, say 60° and 70°, whose sum is less than 180°. Let the included side be 5 cm. What could the measure of the third angle be? Does this measure change if the base length is changed to some other value, say 7 cm? Construct and find out.
53. In general, once the two angles are fixed, does the third angle depend on the included sidelength? Try with different pairs of angles and lengths.
54. Try experimenting with different triangles to see if there is a relation between any two angles and the third one. To find this relation, what data will you keep track of and how will you organise the data you collect?
55. Consider a triangle ABC with ∠B = 50° and ∠C = 70°. Let us suppose we construct a line XY parallel to BC through vertex A. We can see new angles being formed here: ∠XAB, and ∠YAC. What are their values? Can we find ∠BAC from this?
56. Find the third angle of a triangle (using a parallel line) when two of the angles are: (a) 36°, 72° (b) 150°, 15° (c) 90°, 30° (d) 75°, 45°
57. Can you construct a triangle all of whose angles are equal to 70°? If two of the angles are 70° what would the third angle be? If all the angles in a triangle have to be equal, then what must its measure be? Explore and find out.
58. Here is a triangle in which we know ∠B = ∠C and ∠A = 50°. Can you find ∠B and ∠C?
59. What can we say about the sum of the angles of any triangle? (Consider a triangle ABC and construct a line through A that is parallel to BC.)
60. There is a convenient way of verifying the angle sum property by folding a triangular cut-out of a paper. Do you see how this shows that the sum of the angles in this triangle is 180°?
61. Find ∠ACD, if ∠A = 50°, and ∠B = 60°.
62. Find the exterior angle for different measures of ∠A and ∠B. Do you see any relation between the exterior angle and these two angles? [Hint: From angle sum property, we have ∠A + ∠B + ∠ACB = 180°.] We also have ∠ACD + ∠ACB = 180°, since they form a straight angle. What does this show?
63. Consider a triangle ABC. What is the height of the vertex A from its opposite side BC, and how can it be measured?
64. What would the altitude from A to BC be in this triangle? (a triangle in which the angle at B is obtuse)
65. Cut out a paper triangle. Fix one of the sides as the base. Fold it in such a way that the resulting crease is an altitude from the top vertex to the base. Justify why the crease formed should be perpendicular to the base.
66. Construct an arbitrary triangle. Label the vertices A, B, C taking BC to be the base. Construct the altitude from A to BC. Can you see how to do this?
67. Does there exist a triangle in which a side is also an altitude? Visualise such a triangle and draw a rough diagram.
68. Did you spot any other type of triangle?
69. What are the other types of triangles based on angle measures?
70. What could an acute-angled triangle be? Can we define it as a triangle with one acute angle? Why not?
71. Construct a triangle ABC with BC = 5 cm, AB = 6 cm, CA = 5 cm. Construct an altitude from A to BC.
72. Construct a triangle TRY with RY = 4 cm, TR = 7 cm, ∠R = 140°. Construct an altitude from T to RY.
73. Construct a right-angled triangle ∆ABC with ∠B = 90°, AC = 5 cm. How many different triangles exist with these measurements? [Hint: Note that the other measurements can take any values. Take AC as the base. What values can ∠A and ∠C take so that the other angle is 90°?]
74. Through construction, explore if it is possible to construct an equilateral triangle that is (i) right-angled (ii) obtuse-angled. Also construct an isosceles triangle that is (i) right-angled (ii) obtuse-angled.
75. There is a spider in a corner of a box. It wants to reach the farthest opposite corner (marked in the figure). Since it cannot fly, it can reach the opposite point only by walking on the surfaces of the box. What is the shortest path it can take? Take a cardboard box and mark the path that you think is the shortest from one corner to its opposite corner. Compare the length of this path with that of the paths made by your friends.

Chapter at a Glance

• A triangle has three vertices, three sides and three angles. It is named by its vertices in any order — ∆ABC, ∆BAC and ∆CAB are the same triangle.
• Two arcs drawn with a compass meet at the third vertex, so a triangle whose three sidelengths are known can be constructed exactly, without trial and error.
• Triangle inequality: a triangle exists for three lengths exactly when each length is less than the sum of the other two. It is enough to test the longest length.
• A triangle can also be built from two sides and the included angle , or from two angles and the included side — the latter only when the two angles add to less than 180°.
• Angle sum property: the three angles of any triangle add up to 180°. The proof draws a line through one vertex parallel to the opposite side.
• An altitude is the perpendicular from a vertex to the opposite side; in an obtuse triangle the base has to be extended to receive it.
• Triangles are classified by sides as equilateral, isosceles and scalene, and by angles as acute-angled, right-angled and obtuse-angled.

How to Download NCERT Solutions for Class 7 Maths Chapter 7 PDF

Follow these simple steps to get the a Tale of Three Intersecting Lines questions-and-answers PDF from Ganita Prakash.

1. Search NCERT Solutions for Class 7 Maths Chapter 7 aglasem and open this page.
2. Read the exercise questions with answers for a Tale of Three Intersecting Lines shown above.
3. Click the Download PDF link to save the a Tale of Three Intersecting Lines solutions to your device.

NCERT Solutions for Class 7 Maths – All Chapters

There are more chapters to study besides a Tale of Three Intersecting Lines in Maths. Here are the NCERT Solutions for all chapters of Class 7 Maths.

• Chapter 1 Large Numbers Around Us
• Chapter 2 Arithmetic Expressions
• Chapter 3 a Peek Beyond the Point
• Chapter 4 Expressions Using Letter Numbers
• Chapter 5 Parallel and Intersecting Lines
• Chapter 6 Number Play
• Chapter 7 a Tale of Three Intersecting Lines
• Chapter 8 Working with Fractions

NCERT Solutions for Class 7 – All Subjects

Just like Chapter 7 of Maths, you can get the exercise questions with answers for every other subject of Class 7. Here are the NCERT Solutions for all subjects of Class 7.

• English
• Hindi
• Maths
• Sanskrit
• Science
• Social Science

NCERT Solutions for Class 7 Maths Chapter 7 – An Overview

The key highlights of this study material are as follows.

Aspects	Details
Class	Class 7
Subject	Maths
Chapter Number	Chapter 7
Chapter Name	a Tale of Three Intersecting Lines
Book Name	Ganita Prakash
Book By	NCERT (National Council of Educational Research and Training)
Educational Resource Here	NCERT Solutions of Class 7 Maths Chapter 7 for all exercises
More Questions Answers of This Subject	NCERT Solutions for Class 7 Maths
Download Book Chapter	NCERT Book Class 7 Maths
All Questions Answers For This Class	NCERT Solutions for Class 7
Complete Solutions	NCERT Solutions

NCERT Solutions for Class 7 Maths Chapter 7 a Tale of Three Intersecting Lines – FAQs

What are the NCERT Solutions for Class 7 Maths Chapter 7 a Tale of Three Intersecting Lines?

They are the complete, step-by-step answers to all the exercise and in-text questions of Chapter 7 a Tale of Three Intersecting Lines from the NCERT Class 7 Maths textbook Ganita Prakash, written by experts as per the latest NCERT syllabus.

How can I download the Class 7 Maths Chapter 7 solutions PDF for free?

Open this page on aglasem, read the a Tale of Three Intersecting Lines questions with answers, and click the “Download Solutions PDF” link. The Class 7 Maths Chapter 7 NCERT Solutions PDF is completely free to download.

Are these NCERT Solutions as per the latest 2026-27 syllabus?

Yes. The NCERT Solutions for Class 7 Maths Chapter 7 are based on the latest NCERT textbook Ganita Prakash and the current 2026-27 CBSE syllabus, so the questions and answers match what you study in class.

Where can I get NCERT Solutions for the other chapters of Class 7 Maths?

You can find the answers to every chapter on the NCERT Solutions for Class 7 Maths page, and solutions for every subject on the NCERT Solutions for Class 7 page.

How do NCERT Solutions help in exam preparation?

They show the correct method to solve each question, help you write answers the way they are expected in exams, let you check and correct your own work, and save revision time — which together improve your marks in Class 7 Maths.

If you have any queries on NCERT Solutions for Class 7 Maths Chapter 7 a Tale of Three Intersecting Lines, then please ask in the comments below.