 NCERT Solutions for Class 9 Maths Chapter 7 Triangles all exercises in English Medium and Hindi Medium updated for new academic session 2023-24. As per the new updated syllabus, there are only three exercises in latest NCERT books for CBSE 2023-24.
Class 9 Maths Chapter 7 Solutions in English Medium
Class 9 Maths Exercise 7.1 in English
Class 9 Maths Exercise 7.2 in English
Class 9 Maths Exercise 7.3 in English
In addition to solutions, Tiwari Academy may offer a wide range of practice problems and exercises related to each topic. This gives students ample opportunities to practice and apply what they’ve learned, which is essential for improving problem-solving skills.
Class 9 Maths Chapter 7 Solutions in Hindi Medium
Class 9 Maths Exercise 7.1 in Hindi
Class 9 Maths Exercise 7.2 in Hindi
Class 9 Maths Exercise 7.3 in Hindi

## NCERT Solutions for Class 9 Maths Chapter 7

 Class: 9 Mathematics Chapter: 7 Triangles Number of Exercises: 3 (Three) Content Type: Text and Videos Academic Session: CBSE 2023-24 Medium: English and Hindi Medium According to Utter Pradesh Board (Prayagraj) students of class 9 will use NCERT Books for 9th Maths as course books. So, UP Board Solutions for Class 9 Maths Tribhuj ki Prashnavali 7.1, Prashnavali 7.2 and Prashnavali 7.3 in Hindi Medium PDF format are given to free download for academic session 2023-24. NCERT Solutions (https://ncert.nic.in/) in Hindi Medium and English Medium or View in Video Format, for the students studying NCERT Books 2023-24, are based on the CBSE Curriculum 2023-24. Questions and solutions of all the five exercise of 9th Maths Chapter 7 are given below. Steps for solving questions are described properly by subject experts. Easy and simplified solutions are given, so that student can understand easily.

### 9th Maths Chapter 7 Solutions in English & Hindi Medium

NCERT Solutions for class 9 Maths chapter 7 all exercises in English & Hindi medium free download for session 2023-24. Download UP Board App Apk and NCERT Solutions Offline Apps 2023-24 updated on the basis of NCERT Books 2023-24 free to use offline. ### What are the properties of a Triangle?

Properties of a Triangle
1. Angle opposite to equal sides of an isosceles triangle are equal.
2. The sides opposite to equal angles of a triangle are equal.
3. If two sides of a triangle are unequal then the angle opposite to the longer side is larger.
4. In any triangle, the side opposite to the larger angle is larger.
5. The sum of any two sides of a triangle is greater than the third side.
6. The difference between any two sides of a triangle is less than its third side.
7. If the bisector of the vertical angle of a triangle bisects the base, then triangle is an isosceles triangle.
8. The sum of any two sides of a triangle is greater than twice the median drawn to the third side.

### Define a Triangle.

Triangle: A plane figure closed by three intersecting lines is called a triangle. Here, ‘Tri’ means THREE. A triangle has three sides, three angles and three vertices.

#### Important Notes on 9th Maths Chapter 7

Rules for Congruence of Triangle: Two triangles are congruent, if sides and angles of one triangle are equal to the corresponding sides and angles of the other triangle.
SSS (Side – Side – Side) Congruence Rule: Two triangles are congruent, if three sides of one triangle are equal to three sides of the other triangle.
RHS (Right angle – Hypotenuse – Side) Congruence Rule: Two right triangles are congruent, if the hypotenuse and one side of one triangle are equal to hypotenuse and one side of the other triangle.
ASA (Angle – Side – Angle) Congruence Rule: Two triangles are congruent, if two angles and the included side of one triangle are equal to two angles and the included side of the other triangle.
SAS (Side – Angle – Side) Congruence Rule: Two triangles are congruent, if two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle.

### ABC is a triangle. Locate a point in the interior of ΔABC which is equidistant from all the vertices of ΔABC.

Draw perpendicular bisectors of AB, BC and AC, which intersects each other at G. Point G is equidistant from the three vertices of ΔABC.

### In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.

Draw the bisectors of ∠A, ∠B and ∠C, which intersect each other at O. Point O is equidistant from the three sides of ΔABC i.e. OP = OQ = OR.

### AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that AD bisects BC.

In ΔABD and ΔACD, ∠ADB = ∠ADC [∵ Each 90°] AB = AC [∵ Given] AD = AD [∵ Common] Hence, ΔABD ≅ ΔACD [∵RHS Congruency Rule] BD = DC [∵ CPCT] Hence, AD bisects BC

### ABC is an isosceles triangle with AB = AC. Draw AP ⊥ BC to show that ∠B = ∠C.

In ΔABP and ΔACP, ∠APB = ∠APC [∵ Each 90°] AB = AC [∵ Given] AP = AP [∵ Common] Hence, ΔABP ≅ ΔACP [∵RHS Congruency Rule] ∠B = ∠C [∵ CPCT]

### What are the main points of chapter 7 of class 9th Maths that students must remember at the exam time?

The main points of chapter 7 of class 9th Maths that students must remember at the time of exam are:

1. Two figures are congruent, if they are of the same shape and of the same size.
2. If two triangles ABC and PQR are congruent under the correspondence A ↔ P, B ↔ Q and C ↔ R, then symbolically, it is expressed as ∆ ABC ≅ ∆ PQR.
3. 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 (SAS Congruence Rule).
4. 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 (ASA Congruence Rule).
5. 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 (AAS Congruence Rule).
6. Angles opposite to equal sides of a triangle are equal.
7. Sides opposite to equal angles of a triangle are equal.
8. If three sides of one triangle are equal to three sides of the other triangle, then the two triangles are congruent (SSS Congruence Rule).
9. 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 (RHS Congruence Rule).
10. In a triangle, angle opposite to the longer side is larger (greater).
11. In a triangle, side opposite to the larger (greater) angle is longer.
12. Sum of any two sides of a triangle is greater than the third side.

### Does chapter 7 of grade 9th Maths contain any optional exercise? If yes, which exercise of chapter 7 is optional?

As per the new syllabus, the chapter 7 of grade 9th Maths contains no optional exercise. Earlier, there were five exercises in chapter 7 and the last exercise (Exercise 7.5) was the optional one. Now there are only three exercises in course and all are important for examination point of view.

### Is chapter 7 Triangles of class 9th Maths easy or difficult to solve?

Chapter 7 of class 9th Maths is not easy and not difficult. It lies in the middle of easy and difficult because some examples and questions of this chapter are easy, and some are complicated. However, the difficulty level of any topic varies from student to student. So, Chapter 7 of class 9th Maths is easy or not depends on students also. Some students find it difficult, some find it easy, and some find it in the middle of easy and tough.

### What are the real-life examples of congruent shapes in 9th Maths Chapter 7?

Some real-life examples of congruent shapes are:

1. Pair of earrings.
2. Pages of the same book.
3. Biscuits of the same packs.
4. Two bangles of the same radii.
5. Two square sheets of the same sides.
Last Edited: September 18, 2023