NCERT Solutions for Class 7 Mathematics Chapter 5 Parallel and Intersecting Lines
NCERT Solutions for Class 7 Mathematics Chapter 5 Parallel and Intersecting Lines
NCERT Solutions for Class 7 Mathematics Chapter 5 Parallel and Intersecting Lines
This worksheet provides complete and accurate NCERT Solutions for Class 7 Mathematics Chapter Parallel and Intersecting Lines. It helps students understand how lines behave when they meet or do not meet on a plane surface. The chapter is important because it builds a strong foundation in geometry concepts such as angles, parallel lines, perpendicular lines, and transversals. These solutions strictly follow the NCERT pattern and ensure clarity, accuracy, and proper understanding for school students and parents.
Chapter summary: stories, poems & themes
This chapter is fully concept-based and activity-based. It includes hands-on activities like drawing intersecting lines, paper folding, and observing patterns on dot grids. Students learn how angles are formed when lines intersect and how different types of lines relate to each other. The main focus of the chapter is understanding geometric relationships such as linear pairs, vertically opposite angles, parallel lines, perpendicular lines, and transversals through observation and practice.
What this NCERT chapter covers?
• Understanding intersecting lines and angles formed
• Concept of linear pairs and vertically opposite angles
• Identification of parallel and perpendicular lines
• Observation of patterns through paper folding activities
• Understanding transversals and angle relationships
• Application of corresponding angles and angle properties
• Visual and activity-based learning using diagrams and dot grids
How to use these NCERT solutions?
Students should first try solving the questions on their own by carefully observing diagrams and applying concepts. After attempting, they can use these NCERT Solutions to check their answers step by step. Parents and teachers can guide students by explaining reasoning behind each solution. These answers follow the exact NCERT sequence, making revision easier and helping students understand concepts clearly.
Student tips & learning tricks
• Always draw neat diagrams to understand line relationships clearly
• Remember that vertically opposite angles are always equal
• Linear pairs always add up to 180 degrees
• Parallel lines never meet and remain equidistant
• Use rulers and protractors carefully to avoid measurement errors
• Practice identifying corresponding and alternate angles in diagrams
Why NCERT solutions are important?
NCERT Solutions help students build strong conceptual clarity and confidence in mathematics. They follow the exact syllabus and exam pattern, making them reliable for school assessments. These solutions ensure proper understanding of geometry basics, which are essential for higher classes. Regular practice with accurate NCERT answers improves problem-solving skills and logical thinking.
Complete answer key – NCERT solutions
Activity 1 (Page 107)
Explanation: Draw different pairs of intersecting lines on paper. Measure all four angles formed using a protractor. Compare the angles and observe relationships like equal opposite angles and angles forming a straight line.
1. No. A pair of straight lines can intersect at only one point.
2. ∠a = ∠c and ∠b = ∠d (vertically opposite angles are equal)
∠a + ∠b = 180°, ∠b + ∠c = 180° (linear pairs)
3. Yes, always true for intersecting lines
Figure it Out (Page 108)
Linear pairs:
1. ∠a & ∠b
2. ∠b & ∠c
3. ∠c & ∠d
4. ∠d & ∠a
Vertically opposite angles:
1. ∠a & ∠c
2. ∠b & ∠d
Explanation: student-generated activity
Parallel lines (Page 110)
Parallel lines in Fig. 5.6:
1. a ∥ i ∥ h
2. c ∥ g
3. d ∥ f
4. e ∥ b
Fill in the blanks:
1. Opposite edges → Parallel
2. Adjacent edges → Perpendicular
After folds:
1. 1st fold → 3 parallel lines
2. 2nd fold → 5 parallel lines
3. 3rd fold → 9 parallel lines
Activity 2 (Page 111)
Explanation: student-generated activity
Activity (Page 112)
Answer: Yes
1. a ∥ p
2. b ∥ q
3. c ∥ r
Reason: Same direction and equal spacing (parallel lines)
Figure it Out (Page 113-114)
1. Lines drawn at 90° to given lines (student-generated activity)
2. a. They form 90° angle
b. Lines remain equidistant and never meet
3. Sample answer (student-generated activity)
4. 1. Yes
2. Difficult ones → e, f, g, h
3. Draw by keeping equal distance
5.
Ans. Line c is parallel to line a
Reason: Equal distance, same direction
(Page 115)
Answer: 1. No (vertically opposite angles are equal)
2. No (again due to equal pairs)
Figure it Out (Page 119)
Explanation: student-generated activity
(Page 120)
Answer: Both are perpendicular to same line (t)
Corresponding angles = 90°
Therefore parallel
Figure it Out (Page 123-125)
1. a = 48°
b = 52°
c = 81°
d = 99°
e = 69°
f = 48°
g = 122°
h = 75°
i = 54°
j = 97°
2. (i) a = 138 degrees
(ii) a = 118 degrees
(iii) a = 105 degrees
(iv) a = 23 degrees
3. (i) x = 25 degrees, y = 155
(ii) x = 25 degrees
4. GEH = 45 degrees
HEF = 57 degrees
FED = 78 degrees
5. x = 125 degrees
y = 125 degrees
6. ∠NOP = 108 degrees
Parallel Illusions
Explanation: In these pictures, the lines may look like they are not parallel because of surrounding patterns and designs. Our eyes get confused due to angles and spacing, but in reality, many lines are parallel. This shows that visual observation can be misleading.
Summary
The summary explains how lines behave when they intersect and form different angles. It covers important concepts like parallel lines, perpendicular lines, and transversals. It helps students quickly revise all key properties and relationships of lines and angles. :contentReference[oaicite:0]{index=0}
Master Class 7 Mathematics with accurate NCERT Solutions and step-by-step explanations designed for strong conceptual learning.