# NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Ex 7.4) Exercise 7.4

## NCERT Solutions for Class 9 Maths Chapter 7 Triangles (Ex 7.4) Exercise 7.4

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Q1: What are the theorems covered in this exercise?

A1: Exercise 7.4 covers the theorem related to the topic “Inequalities in a Triangle” and questions related to it. There are 3 theorems that are exclusively explained in this exercise. These are as follows

Theorem 7.6: If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater).

Theorem 7.7: In any triangle, the side opposite to the larger (greater) angle is longer.

Theorem 7.8: The sum of any two sides of a triangle is greater than the third side.

Exercise 7.4 contains a total of 6 questions. All the questions are based on the above-mentioned theorems. Students must, therefore, ensure that they are quite well versed in the above theorems before answering the questions. Also, students must practice the theorem consistently and learn to apply them. There are a total of 6 questions in this exercise which will help students understand and practise these theorems better.

Q2: What are the concepts of triangles that students learn in this chapter?

A2: Given below are the concepts covered in Chapter 6 – The Triangle and its Properties of Class 7 Maths NCERT Solutions. The chapter contains a total of 5 exercises covering problems related to the following concepts.

Medians of a Triangle

Altitudes of a Triangle

Exterior Angle of a Triangle and Its Property

Angle Sum Property of a Triangle

Two Special Triangles: Equilateral and Isosceles

Sum of the Lengths of Two Sides of A Triangle

Right-Angled Triangles and Pythagoras Property

Q3: ABC is a triangle, right-angled at C. If AB = 25 cm and AC = 7 cm, find BC.

A3: AB = 5 cm, AC = 4 cm

Let BC be x cm.

In right angled triangle ACB,

(Hypotenuse)^{2} = (Base)^{2} + (Perpendicular)^{2} [By Pythagoras theorem]

(AB)^{2} = (AC)^{2} + (BC)^{2}

5^{2} = 4^{2} + x^{2}

25 = 16+ x^{2}

x^{2} = 25 – 16 = 9

x = 3cm

Thus, the length of BC is 24 cm.

Q4: What are the various exercises in chapter 7?

A4: The various exercises available for this chapter along with the number of questions present in them for the students to solve is given below:

Exercise 7.1 - 8 Questions - 6 Short Answer Questions, 2 Long Answer Questions.

Exercise 7.2 Solution 8 Questions (6 Short Answer Questions, 2 Long Answer Question)

Exercise 7.3 Solution 5 Questions (3 Short Answer Questions, 2 Long Answer Question)

Exercise 7.5 (Optional) Solution 4 Questions

Students can also have a look at the NCERT Solutions of Class 9 for Maths subject and other NCERT study material and notes available on the Vedantu website for enhancing their exam preparation. Also, all the answers for the above exercise questions along with detailed step by step explanations are given in the NCERT Solutions for Class 9 Maths.