NCERT Solutions Class 7 Maths Chapter 6 The Triangle and its Properties Exercise 6.4

The NCERT Solutions Class 7 Maths Chapter 6: The Triangle and its Properties, Exercise 6.4, presents one of the most basic principles in geometry: the Triangle Inequality Theorem. The Triangle Inequality establishes the condition required in order for any three line segments to exist as a closed triangle.

In this exercise, students will apply the Triangle Inequality Theorem to see whether or not it is possible to imagine a triangle with a given set of side lengths, and they will use inequality to establish relationships between the medians of triangles and the diagonals of quadrilaterals. It reinforces logical reasoning and prepares students for geometric proofs in high school.

1.0Download Class 7 Maths Chapter 6 Ex 6.4 NCERT Solutions PDF

Learn how to construct any triangle according to any rule! Download the complete NCERT Solutions for this exercise with step-by-step instructions. The NCERT Solutions for Class 7 Maths Chapter 6 contain proofs and logical explanations for the geometric inequalities.

2.0Key Concepts of Exercise 6.4

• Triangle Inequality Theorem: The length of any two sides of a triangle cannot be possible if the sum is equal to or less than the length of the third side. 
• For segments: a,b,c: a+b>c, a+c>b, b+c>a..
• Length of Side: The length of the third side must also be:
• Less than the sum of the other two segments.
• Greater than the difference between the two segments.
• Medians and Perimeters: We can apply the inequality theorem to triangles made by a median to show that the perimeter of the original triangle is greater than twice the

3.0CBSE Class 7 Chapter 6 Exercise 6.4 Comprises

• Feasibility Check: Assessing whether a triangle can exist with the three specified side lengths.
• Interior Point Inequalities: Verifying inequalities when a point is chosen in the interior of a triangle (△OPQ in the interior of △PQR) using the theorem.
• Perimeter and Medians Proofs: To demonstrate inequalities related to a triangle's perimeter and that of its medians.
• Quadrilateral Proofs: To extend the theorem to demonstrate that the sum of the sides of a quadrilateral will exceed the sum of the diagonals of that quadrilateral.

4.0NCERT Solutions Class 7 Maths Chapter 6 Number Play : Other Exercises

5.0Detailed NCERT Class 7 Chapter 6 Exercise 6.4 Solutions

1. Using the generalised form, find a magic square if the centre number is 25 .

Sol. A magic square with the center value 25 , where other numbers in the grid are expressed in relation to 25 .

2. What is the expression obtained by adding the 3 terms of any row, column or diagonal?

Sol. Row sum (1st  row )=28+21+26=75

Column sum (1st  column )=28+23+24=75

Diagonal sum (1st  column )=28+25+22=75

The expression obtained =3×m where m is the letter-number representing the number in the centre.

3. Write the result obtained by-

(a) adding 1 to every term in the generalised form.

(b) doubling every term in the generalised form

Sol.

original

(a)

(b)

4. Create a magic square whose magic sum is 60 .

Sol. A 3×3 magic square's sum is 3× the middle element.

So, for a sum of 60 , the middle element should be 360​=20

To get a magic sum of 60 , we will multiply the original magic square by 4 , i.e.,

 5. Is it possible to get a magic square by filling nine non-consecutive numbers?

Sol. Yes, it is possible. Let us consider the two magic squares with a magic sum 45.

9 consecutive numbers:

9 non consecutive numbers:

6.0Key Features and Benefits: Class 7 Maths Chapter 6 Exercise 6.4

• Fundamental Geometry: Proves the most important condition needed for a polygon to exist.
• Inequality Reasoning: Shows how to use the inequality symbols (> and <) in a proof statement.
• Real Life Relevance: Justifies why the direct path between two points (a single side of a triangle) is always shorter than the indirect path (the sum of the two other sides).