NCERT Solutions for Class 7 Maths Chapter 5 Parallel and Intersecting Lines provide clear, step-by-step answers to every exercise and in-text question from the chapter Parallel and 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 5 question-answer PDF.
NCERT Solutions for Class 7 Maths Chapter 5 Parallel and Intersecting Lines
- Class: Class 7
- Subject: Maths
- Chapter: Chapter 5 – Parallel and Intersecting Lines
- Textbook: Ganita Prakash (NCERT)
- Study material: NCERT Solutions – questions with answers, free PDF
These solutions answer all the exercise questions of Chapter 5 Parallel and 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 5 Parallel and Intersecting Lines View Download
NCERT Solutions for Class 7 Maths Chapter 5 PDF Download
You can read the NCERT Solutions for Class 7 Maths Chapter 5 online above, or download the complete question-answer PDF to study Parallel and Intersecting Lines offline at any time.
NCERT Solutions for Class 7 Maths Chapter 5 PDF Download Link – Click Here to Download Solutions PDF
Questions Covered in This Chapter
These NCERT Solutions answer all 55 questions of this chapter. The questions solved are:
- Take a piece of square paper and fold it in different ways. Now, on the creases formed by the folds, draw lines using a pencil and a scale. You will notice different lines on the paper. Take any pair of lines and observe their relationship with each other. Do they meet? If they do not meet within the paper, do you think they would meet if they were extended beyond the paper?
- Let us observe what happens when two lines intersect. How many angles do they form?
- Can two straight lines intersect at more than one point?
- Activity 1: Draw two lines on a plain sheet of paper so that they intersect. Measure the four angles formed with a protractor. Draw four such pairs of intersecting lines and measure the angles formed at the points of intersection. What patterns do you observe among these angles?
- In Fig. 5.2, if ∠a is 120°, can you figure out the measurements of ∠b, ∠c and ∠d, without drawing and measuring them?
- Is this always true for any pair of intersecting lines? Check this for different measures of ∠a. Using these measurements, can you reason whether this property holds true for any measure of ∠a?
- List all the linear pairs and vertically opposite angles you observe in Fig. 5.3: Linear Pairs — ∠a and ∠b, … ; Pairs of Vertically Opposite Angles — ∠b and ∠d, …
- Can you draw a pair of intersecting lines such that all four angles are equal? Can you figure out what will be the measure of each angle?
- Observe Fig. 5.5 and describe the way the line segments meet or cross each other in each case, with appropriate mathematical words (a point, an endpoint, the midpoint, meet, intersect) and the degree measure of each angle. For example, line segments FG and FH meet at the endpoint F at an angle 115.3°.
- Are line segments ST and UV likely to meet if they are extended?
- Are line segments OP and QR likely to meet if they are extended?
- Name some parallel lines you can spot in your classroom.
- Which pairs of lines appear to be parallel in Fig. 5.6 below?
- Take a plain square sheet of paper (use a newspaper for this activity). How would you describe the opposite edges of the sheet? They are _________________________ to each other.
- How would you describe the adjacent edges of the sheet? The adjacent edges are _________________________ to each other. They meet at a point. They form right angles.
- Fold the sheet horizontally in half. A new line is formed (see Fig. 5.7). How many parallel lines do you see now? How does the new line segment relate to the vertical sides?
- Make one more horizontal fold in the folded sheet. How many parallel lines do you see now?
- What will happen if you do it once more? How many parallel lines will you get? Is there a pattern? Check if the pattern extends further, if you make another horizontal fold.
- Make a vertical fold in the square sheet. This new vertical line is ___________ to the previous horizontal lines.
- Fold the sheet along a diagonal. Can you find a fold that creates a line parallel to the diagonal line?
- Take a square sheet of paper, fold it in the middle and unfold it. Fold the edges towards the centre line and unfold them. Fold the top right and bottom left corners onto the creased line to create triangles. Refer to Fig. 5.8. The triangles should not cross the crease lines. Are a, b and c parallel to p, q and r respectively? Why or why not?
- Draw some lines perpendicular to the lines given on the dot paper in Fig. 5.10.
- In Fig. 5.11, 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?
- 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.
- 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?
- In Fig. 5.13, which line is parallel to line a — line b or line c? How do you decide this?
- Is it possible for all the eight angles to have different measurements? Why, why not?
- What about five different angles — 6, 5, 4, 3 and 2?
- In Fig. 5.14, since ∠1 and ∠3 are vertically opposite angles, they are equal. Are there other pairs of vertically opposite angles?
- Activity 3: Draw a pair of lines and a transversal such that they form two distinct angles. Step 1: Draw a line l and a transversal t intersecting it at point X. Step 2: Measure ∠a formed by lines l and t (let us say it is 60°). Step 3: Mark a point Y on line t. Step 4: Draw a line m through point Y that forms a 60° angle to line t.
- How many distinct angles have formed now?
- What do you observe about lines l and m? Do they appear to be parallel to each other?
- Activity 4: Fig. 5.19 has a pair of parallel lines l and m (what is the notation used in the figure to indicate they are parallel?). Line t is the transversal across these two lines.
- Take a tracing paper and trace ∠a on it. Now place this tracing paper over ∠b and see if the angles align exactly. Check the other corresponding angles in the figure using a protractor. Are all the corresponding angles equal to each other?
- Activity 5: In Fig. 5.20, draw a transversal t to the lines l and m such that one pair of corresponding angles is equal. You can measure the angles with a protractor. Are you finding it hard to draw a transversal such that the corresponding angles are equal?
- Can you draw a pair of parallel lines using a ruler and a set square? Fig. 5.21 shows how you can do it. Draw a line l with a scale. By sliding your set square you can make two lines perpendicular to line l.
- Are these two lines parallel to each other? How are we sure that they are parallel to each other? What angles are formed between these lines and line l?
- Draw two more parallel lines using the long side of the set square as shown in Fig. 5.22.
- How do you know these two lines are parallel? Can you check if the corresponding angles are equal?
- 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.
- Why are lines l and m parallel to each other? (Making Parallel Lines through Paper Folding, Fig. 5.24)
- Activity 6: In Fig. 5.25, if ∠f is 120° what is the measure of its alternate angle ∠d?
- Example 1: In Fig. 5.26, parallel lines l and m are intersected by the transversal t. If ∠6 is 135°, what are the measures of the other angles?
- Example 2: In Fig. 5.27, lines l and m are intersected by the transversal t. If ∠a is 120° and ∠f is 70°, are lines l and m parallel to each other?
- Example 3: In Fig. 5.28, parallel lines l and m are intersected by the transversal t. If ∠3 is 50°, what is the measure of ∠6?
- Is there a relation between ∠3 and ∠6? You could try to find the relationship by taking different values for ∠3 and see what ∠6 is. Once you find a relation, try to justify it or prove that this relation holds always.
- Example 4: In Fig. 5.29, line segment AB is parallel to CD and AD is parallel to BC. ∠DAC is 65° and ∠ADC is 60°. What are the measures of angles ∠CAB, ∠ABC, and ∠BCD?
- Find the angles marked below. (Fig. 5.30 — a, b, c, d, e, f, g, h, i and j)
- Find the angle represented by a. (Fig. 5.31 — four figures)
- In the figures below, what angles do x and y stand for? (Fig. 5.32)
- In Fig. 5.33, ∠ABC = 45° and ∠IKJ = 78°. Find angles ∠GEH, ∠HEF, ∠FED
- In Fig. 5.34, AB is parallel to CD and CD is parallel to EF. Also, EA is perpendicular to AB. If ∠BEF = 55°, find the values of x and y.
- What is the measure of angle ∠NOP in Fig. 5.35? [Hint: Draw lines parallel to LM and PQ through points N and O.]
- There do not seem to be any parallel lines here. Or, are there?
- What causes these illusions?
Chapter at a Glance
- When two lines intersect, four angles are formed. Linear pairs add up to 180° and vertically opposite angles are equal.
- If all four angles at a crossing are equal, each is 90° and the lines are perpendicular .
- Parallel lines lie in the same plane and never meet, however far they are extended. They are marked with matching arrow heads.
- A transversal cutting two lines makes 8 angles, with at most 4 different sizes.
- Corresponding angles are equal exactly when the two lines are parallel — this is the test for parallelism.
- For a transversal across parallel lines: alternate angles are equal, and interior angles on the same side add up to 180°.
How to Download NCERT Solutions for Class 7 Maths Chapter 5 PDF
Follow these simple steps to get the Parallel and Intersecting Lines questions-and-answers PDF from Ganita Prakash.
- Search NCERT Solutions for Class 7 Maths Chapter 5 aglasem and open this page.
- Read the exercise questions with answers for Parallel and Intersecting Lines shown above.
- Click the Download PDF link to save the Parallel and Intersecting Lines solutions to your device.
NCERT Solutions for Class 7 Maths – All Chapters
There are more chapters to study besides Parallel and 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 5 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.
NCERT Solutions for Class 7 Maths Chapter 5 – An Overview
The key highlights of this study material are as follows.
| Aspects | Details |
|---|---|
| Class | Class 7 |
| Subject | Maths |
| Chapter Number | Chapter 5 |
| Chapter Name | Parallel and 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 5 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 5 Parallel and Intersecting Lines – FAQs
What are the NCERT Solutions for Class 7 Maths Chapter 5 Parallel and Intersecting Lines?
They are the complete, step-by-step answers to all the exercise and in-text questions of Chapter 5 Parallel and 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 5 solutions PDF for free?
Open this page on aglasem, read the Parallel and Intersecting Lines questions with answers, and click the “Download Solutions PDF” link. The Class 7 Maths Chapter 5 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 5 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 5 Parallel and Intersecting Lines, then please ask in the comments below.
