 # NCERT Solutions for Class 9 Maths Chapter 7 Triangles Exercise 7.5 (Optional)

Chapter 7 of NCERT Class 9 Maths ends with Exercise 7.5. Exercise 7.5 is optional, which means that the questions from this exercise will not be asked in the exam. So, now students must be thinking why this exercise is being provided in the NCERT book? The answer is, it is being added to enhance the students’ thinking ability. The chapters in NCERT Maths textbook is not provided just for the sake of passing the exams. The main aim is to generate brilliant students who not only have theoretical knowledge but also have the ability to solve the problems of the real world. So, this exercise is basically meant to check your knowledge about the topics you have learned until now in chapter 7 Triangles.

Students must give equal importance to optional exercise too. Here we have provided the detailed NCERT Solutions for Class 9 Maths Chapter 7 Triangles Exercise 7.5 (Optional). The exercise contains only 4 questions. Try to solve all of them and in case you get stuck somewhere then go through the solution pdf whose link is provided below.

### Download PDF of NCERT Solutions for Class 9 Maths Chapter 7 – Triangles Exercise 7.5

Students can also have a look at the class-wise NCERT Solutions of Class 4 to Class 12 to know the answers of all chapters with detailed explanations.

### Access Answers to NCERT Class 9 Maths Chapter 7 – Triangles Exercise 7.5     ### Access Other Exercise Solutions of Class 9 Maths Chapter 7 – Triangles

Students can have a look at the solution of all the exercise of this chapter by clicking on the link below.

Exercise 7.1 Solution 8 Questions (6 Short Answer Questions, 2 Long Answer Question)

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 7.4 Solution 6 Questions (5 Short Answer Questions, 1 Long Answer Question)

## NCERT Solutions for Class 9 Maths Chapter 7 – Triangles Exercise 7.5 (Optional)

Exercise 7.5 of Chapter 7 Class 9 Maths will recall all the concepts that students have studied in Triangles. To solve the exercise questions students must know the properties of Triangles and theorems very well. Lets summaries it again:

1. Definition of Congruent: Two figures are congruent if they are of the same shape and of the same size.
2. SAS Congruence Rule: If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent.
3. ASA Congruence Rule: If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the two triangles are congruent.
4. AAS Congruence Rule: If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent.
5. SSS Congruence Rule: If three sides of one triangle are equal to three sides of the other triangle, then the two triangles are congruent.
6. RHS Congruence Rule: If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent.
7. Properties of Triangles:
• Sum of any two sides of a triangle is greater than the third side.
• In a triangle, the angle opposite to the longer side is larger (greater).
• In a triangle, the side opposite to the larger (greater) angle is longer.
• Angles opposite to equal sides of a triangle are equal.
• Sides opposite to equal angles of a triangle are equal.
• Each angle of an equilateral triangle is of 60°.

After this, give a try to solve the questions given in Exercise 7.5. Don’t worry if you are not able to solve it. Refer to the solution PDF provided by us. You will get to know the steps to solve the problems easily.

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