# NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.4

Get here all NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.4 Triangles with suitable explanations and examples for first term exam. Questions are well explained in PDF and video format using simplified steps, making class 9 Maths too easy.

Exercise 7.4 of standard 9 Maths solution’s videos are available in Hindi and English Medium free to use or download. Question wise solutions are given in videos with step by step derivation using simple formulae.## Class 9 Maths Exercise 7.4 Solution in Hindi and English

### NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.4 in Hindi and English Medium

Class: 9 | Mathematics |

Chapter: 7 | Triangles |

Exercise: 7.4 | NCERT Solutions in PDF and Videos |

### Class 9 Maths Exercise 7.4 Solution in Hindi Medium Video

#### Class 9 Maths Chapter 7 Exercise 7.4 Solution in Videos

#### Main Points of Class 9 Maths Chapter 7

- If the three sides of one triangle are equal to the other triangle’s three sides, then the two triangles are congruent (SSS Rule).
- If two right triangles, the hypotenuse and one side of a triangle are equal to the hypotenuse, and the other is on one side of the triangle, then the two triangles are congruent (RHS Rule).
- In a triangle, the angle opposite the longest side is greater (larger).
- In a triangle, the side opposite the largest (largest) angle is longer.
- The sum of any two sides of a triangle is greater than the third side.

## Important Example 1 for Exams

D is a point on side BC of Δ ABC such that AD = AC. Show that AB > AD. Solution: In Δ DAC, AD = AC (Given) So, ∠ ADC = ∠ ACD (Angles opposite to equal sides) Now, ∠ ADC is an exterior angle for ΔABD. So, ∠ ADC > ∠ ABD or, ∠ ACD > ∠ ABD or, ∠ ACB > ∠ ABC So, AB > AC (Side opposite to larger angle in Δ ABC) or, AB > AD (AD = AC)

## Example 2 with Solutions for School tests

P is a point equidistant from two lines l and m intersecting at point A. Show that the line AP bisects the angle between them. Solution: You are given that lines l and m intersect each other at A. Let PB ⊥ l, PC ⊥ m. It is given that PB = PC. We have to show that ∠ PAB = ∠ PAC. Now, consider Δ PAB and Δ PAC. In these two triangles, PB = PC (Given) ∠ PBA = ∠ PCA = 90° (Already given in the question) PA = PA (as these are Common) So, Δ PAB ≅ Δ PAC (Using RHS congruency rule) So, ∠ PAB = ∠ PAC (Because these are CPCT)

##### Which theorems, students learn in exercise 7.4 of class 9th Maths?

Students learn three theorems in exercise 7.4 of class 9th Maths, which are:

**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.

##### What is the central concept on which exercise 7.4 of 9th Maths based?

Class 9 Maths exercise 7.4 is based on the concepts of inequalities. Questions are based on the comparison of two angles or two sides, which are unequal.

##### Is exercise 7.4 of grade 9th Maths important from an exam point of view?

Yes, exercise 7.4 of grade 9th Maths is important from an exam point of view. In the exam, two or more than two marks questions can come from this exercise. The most important questions of exercise 7.4 are questions 3, 4, 5, 6.

##### Which example in 9th Maths exercise 7.4 is important for exams?

There is only one example that is example number 9. This example important not only for exams but to understand some other questions also.

##### Can students complete exercise 7.4 of class 9th Maths in 2 days?

Students can complete exercise 7.4 of class 9th Maths in 2 days or not depends on student’s working speed, efficiency, capability, and many other factors. But if they try to complete exercise 7.4 of grade 9th Maths in 2 days, they can do that because there are only 6 questions and one example (example 9) in this exercise.

##### Which is the most challenging question of exercise 7.4 of class 9 Maths?

Question number 3 and 5 are a little bit difficult to understand. These questions need more practice to be confident.

##### Is exercise 7.4 (chapter 7) of class 9 Maths easy to solve?

Exercise 7.4 of class 9 Maths is the easiest exercise. But difficulty level of anything varies from student to student. So, Exercise 7.4 (chapter 7) of class 9th mathematics is easy or not depends on students also.