NCERT Solutions Class 7 Maths Chapter 7 A Tale of Three Intersecting Lines Exercise 7.1

The first exercise consists of core aspects, utilising the Triangle Inequality Theorem and the rules for the existence of a triangle. It assures that students have the mathematical criteria (the "tale") for any three line segments to create a closed triangle. It is just a program.

This exercise introduces the fundamental inequality for sides and the necessary conditions for angles while also allowing students to probe the conditions for simple construction using a compass and ruler.

1.0Download Class 7 Maths Chapter 7 Ex 7.1 NCERT Solutions PDF

Become familiar with the requirements for a triangle to exist with our thorough, step-by-step NCERT Solutions for Class 7 Maths Chapter 7 Exercise 7.1. You can download the free PDF below to practice your skills with geometric reasoning and construction.

2.0Key Concepts of Exercise 7.1 Class 7 Chapter 7 Solutions

• The Triangle Inequality Theorem: The primary relevance is: If a triangle has side lengths, the sum of the lengths of two sides must be greater than the length of the longest third side.

For example, a, b, and c: a + b > c, a + c > b, and b + c > a.

• Triangle Construction Conditions: Recognising that for a triangle to be constructed, all three length-angle-angle must hold true (e.g., the sum of the two smaller sides is greater than the longest side).
• Basic Geometric Construction: Using a compass and ruler to draw triangles accurately (e.g. isosceles or equilateral) based on the given length measurements.
• Assessing the Feasibility: Questions that ask if a triangle can exist given three side lengths are given. 
• Constructing Isosceles or Equilateral Triangles: Use a compass and ruler to draw triangles, sometimes showing that two or three sides are equal (e.g. using the radius of a circle). Issues with Angles: Preliminary questions on the restrictions on angles (e.g. two angles must sum to less than 180 degrees before constructions will work).

3.0NCERT Solutions Class 7 Maths Chapter 7 A Tale of Three Intersecting Lines : Other Exercises

4.0Detailed NCERT Class 7 Chapter 7 Exercise 7.1 Solutions

1. Use the point on the circle and/or the centre to form isosceles triangles.

Sol. The steps of construction are given as

(i) Draw a circle of any radius using compass and denote its centre by 0 .

(ii) Take any two points A and B on the circle and join them to centre 0 .

Then, OA=OB [radii of a circle]

(iii) Now, join AB .

Then the △ABC is the required isosceles triangle.

2. Use the points on the circles and/or their centres to form isosceles and equilateral triangles. The circles are of the same size.

 Sol. (i) Given circles in figure (i) are

Let these two circles intersect at point C and D .

Now, join AB,AC and BC .

Then, AB=AC=AB

[radii of both the circles are same]

Hence, the △ABC is the required equilateral triangle.

We can also construct an isosceles triangle.

Mark a point M on the circle whose centre is at A , out of the shaded region.

Joint AB,AM and BM .

Then, AM=AB

[radii of a circle]

Hence, the △ABM is the required isosceles triangle.

(ii) Given three circles in figure (ii) are

Join points A to B,B to C and A to C .

Observe that AB=BC=CA.

Hence, △ABC is the required equilateral triangle.

We can also construct an isosceles triangle.

Mark a point M on the intersection of the circles whose centre is at A and C, out of the shaded region.

Joint AB,AM and BM .

Then, AM=AB

Hence, the △ABM is the required isosceles triangle.

5.0Key Features and Benefits: Class 7 Maths Chapter 7 Exercise 7.1

• Develops Geometric Reasoning: Allows students to assess the possibility of building a geometric figure before testing it.
• Connects Theory with Practicum: Enables students to see the utilisation of the Triangle Inequality Theorem in practice when using a ruler and compass. 
• Foundation for Congruence: Students need to develop an understanding of how specific lengths and angles must exist for the triangle, which lays the foundation for later lessons on Congruence of Triangles.