NCERT Solutions for Class 7 Mathematics Chapter 7 A Tale of Three Intersecting Lines
NCERT Solutions for Class 7 Mathematics Chapter 7 A Tale of Three Intersecting Lines
NCERT Solutions for Class 7 Mathematics Chapter 7 A Tale of Three Intersecting Lines
This worksheet provides complete and accurate NCERT Solutions for Class 7 Mathematics Chapter A Tale of Three Intersecting Lines. It helps students understand how triangles are formed using different conditions of sides and angles. The chapter is important because it builds a strong foundation in geometry by explaining triangle construction, properties, and conditions for existence. These solutions strictly follow NCERT standards and ensure clarity for both students and parents.
Chapter summary: stories, poems & themes
This chapter is fully activity-based and concept-driven. It includes construction activities using rulers and compasses, along with reasoning-based questions. Students explore how triangles are formed, when they are not possible, and how side lengths and angles affect triangle formation. The main focus is on understanding triangle construction, triangle inequality, and angle properties through practical observation and logical thinking.
What this NCERT chapter covers?
• Construction of triangles using given sides and angles
• Understanding equilateral and isosceles triangles
• Concept of triangle inequality
• Conditions for existence of a triangle
• Relationship between angles and sides in triangles
• Visual and activity-based geometric learning
How to use these NCERT solutions?
Students should first attempt all constructions and reasoning questions on their own using proper tools like ruler and compass. After attempting, they can refer to these NCERT Solutions to verify accuracy. Parents and teachers can guide students in understanding each step logically. These solutions follow the exact NCERT order, making them useful for revision and concept clarity.
Student tips & learning tricks
• Always use a compass carefully for accurate constructions
• Remember that three non-collinear points are required to form a triangle
• Use triangle inequality to check possibility before construction
• Ensure neat diagrams for better understanding
• Check angle sums carefully to avoid mistakes
Why NCERT solutions are important?
NCERT Solutions provide a clear understanding of geometric concepts and improve logical reasoning. They follow the exact syllabus and help students prepare effectively for exams. These solutions strengthen foundational knowledge, making advanced geometry easier to understand in higher classes.
Complete answer key – NCERT solutions
Page 146
Answer: If the three vertices lie on a straight line, no triangle is formed.
Construct a triangle in which all the sides are of length 4 cm:
Construction Steps:
1. Draw a line segment AB = 4 cm
2. With A as centre, draw an arc of radius 4 cm
3. With B as centre, draw another arc of radius 4 cm
4. Let arcs intersect at point C
5. Join AC and BC
6. Triangle ABC is the required triangle
Page 147
The triangle was constructed using:
1. Ruler (to draw line segment)
2. Compass (to draw arcs)
Answer: Because point C lies on both arcs:
Arc from A → AC = 4 cm
Arc from B → BC = 4 cm
Radius of circle = constant
So distances from centre remain fixed
Hence both sides equal
Page 148
Construct a triangle of side lengths 4 cm, 5 cm and 6 cm:
Answer (Steps):
1. Draw AB = 4 cm
2. From A, draw arc radius 5 cm
3. From B, draw arc radius 6 cm
4. Let arcs intersect at C
5. Join AC and BC
Figure it Out (Page 150)
1. Take:
Centre = A
Any two points on the circle = B and C
Join AB and AC
AB = AC (radii of the same circle)
So, triangle ABC has two equal sides
Hence, it is an isosceles triangle
2. Isosceles Triangles:
Take centre A and point B on circle
Take another point C on circle
Join AB, AC, BC
AB = AC (radii)
Triangle ABC is isosceles
Equilateral Triangle:
Take centres A and B
Take intersection point C of the circles
Join AB, BC, CA
AB = BC = CA
Triangle ABC is equilateral
Triangle possibility (Page 151)
i) 3, 4, 8
3 + 4 = 7 < 8
Triangle NOT possible
Figure it Out (Page 154)
1. Answer: Yes, we can check using:
Sum of two sides > third side
2. (a) 10, 10, 25 → Not possible
(b) 5, 10, 20 → Not possible
(c) 12, 20, 40 → Not possible
All fail triangle inequality → No triangle exists
3. Answer: At least two comparisons always satisfy
Largest side is the one that may fail
Figure it Out (Page 156)
1. (a) 2, 2, 5 → Not possible
(b) 3, 4, 6 → Possible
(c) 2, 4, 8 → Not possible
(d) 5, 5, 8 → Possible
(e) 10, 20, 25 → Possible
(f) 10, 20, 35 → Not possible
(g) 24, 26, 28 → Possible
2. Answer: Yes, triangle with sides 50, 50, 50 exists
3. (a) 1, 100
99 < x < 101
Examples: 99.5, 100, 100.5, 99.8, 100.9
Figure it Out (Page 161)
a. Draw AB = 7 cm
At A, construct 75°
Mark AC = 3 cm
Join BC
b. Draw AB = 6 cm
At A, construct 25°
Mark AC = 3 cm
Join BC
c. Draw AB = 8 cm
At A, construct 120°
Mark AC = 3 cm
Join BC
Answer: No — triangle is ALWAYS possible
Two fixed sides + fixed angle
Figure it Out (Page 162)
a. Draw AB = 5 cm
At A → 75°
At B → 75°
Join AC, BC
b. Draw AB = 3 cm
At A → 25°
At B → 60°
Join AC, BC
Answer: Triangle exists when sum of angles < 180°
Examples where triangle is NOT possible:
90° and 90°
100° and 90°
120° and 80°
Figure it Out (Page 163)
1. a. 30°
Possible: 30° + 60°, 30° + 100°
Not possible: 30° + 150°, 30° + 160°
b. 70°
Possible: 70° + 50°, 70° + 100°
Not possible: 70° + 110°, 70° + 120°
c. 54°
Possible: 54° + 60°, 54° + 100°
Not possible: 54° + 126°, 54° + 140°
d. 144°
Possible: 144° + 20°, 144° + 30°
Not possible: 144° + 36°, 144° + 50°
2. a. 35°, 150° → Not possible
b. 70°, 30° → Possible
c. 90°, 85° → Possible
d. 50°, 150° → Not possible
(Page 164)
Given: Angles = 60° and 70°
Third angle = 50°
Answer: No, base length does not affect angles
Explanation: Triangle angles depend only on angle sum property.
Strengthen your understanding of Class 7 Mathematics with reliable NCERT Solutions and step-by-step guidance for better learning.