Class 7 Maths Chapter 7 A Tale of Three Intersecting Lines NCERT Solutions (Step-by-Step Answers, Concepts & Examples | Ganita Prakash)
Class 7 Maths Chapter 7 A Tale of Three Intersecting Lines NCERT Solutions (Step-by-Step Answers, Concepts & Examples | Ganita Prakash)
Introduction
Triangles are the simplest closed shapes in geometry, formed by three sides and three vertices. This chapter explores different types of triangles, their construction methods, and important properties like the triangle inequality and angle sum property.
At FUZY Math Academy, we break down each concept with clear definitions, solved examples, and illustrations to help students retain knowledge effectively.
Key Terms and Definitions
• Triangle: A closed figure with three sides and three angles.
• Equilateral Triangle: All sides equal, all angles equal (60° each).
• Isosceles Triangle: Two sides equal, two angles equal.
• Scalene Triangle: All sides and angles different.
• Triangle Inequality: The sum of any two sides of a triangle must be greater than the third side.
• Angle Sum Property: The sum of the three angles of a triangle is always 180°.
• Exterior Angle: Formed when a side of a triangle is extended outward.
Step‑by‑Step Solved Questions
1. Construct an Equilateral Triangle of side 4 cm
Solution:
1. Draw base AB = 4 cm.
2. With A as center, draw an arc of radius 4 cm.
3. With B as center, draw another arc of radius 4 cm.
4. Intersection point = C.
5. Join AC and BC → △ABC is equilateral.
2. Construct a Triangle with sides 4 cm, 5 cm, 6 cm
Solution:
1. Draw base AB = 4 cm.
2. With A as center, draw an arc of radius 5 cm.
3. With B as center, draw an arc of radius 6 cm.
4. Intersection point = C.
5. Join AC and BC → △ABC is formed.
3. Check if a Triangle Exists with sides 3 cm, 4 cm, 8 cm
Solution:
• Check triangle inequality:
• 3 + 4 = 7 < 8 → ❌ Not possible.
Thus, no triangle can be formed.
4. Angle Sum Property Proof
Solution:
1. Draw △ABC.
2. Through A, draw line XY parallel to BC.
3. ∠XAB = ∠B (alternate angles), ∠YAC = ∠C.
4. ∠A + ∠B + ∠C = 180°.
5. Exterior Angle Example
If ∠A = 50°, ∠B = 60° → ∠C = 70°.
Exterior angle at C = 180° – 70° = 110°.
Notice: Exterior angle = sum of opposite interior angles (50° + 60°).
• Equilateral triangle construction
• Triangle inequality visualization (tent, tree, pole example).
• Angle sum property (parallel line through vertex).
• Exterior angle diagram.
Conclusion
This chapter teaches students not only how to construct triangles but also how to reason about their existence using triangle inequality and angle sum property. By practicing these step‑by‑step methods, students gain confidence in geometry and problem‑solving.
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15 FAQs – Ganita Prakash (Class 7, Chapter 7 A Tale of Three Intersecting Lines)
Step 2: Draw arcs of radius 4 cm from A and B.
Step 3: Intersection point C is the third vertex.
Step 4: Join AC and BC.
Draw arc of radius 5 cm from A and arc of radius 6 cm from B.
Intersection point gives vertex C.
Join AC and BC.
Step 2: Construct given angle at one end.
Step 3: Mark the second side length.
Step 4: Join to form triangle.
Step 2: Construct given angles at both ends.
Step 3: Intersection point gives third vertex.