Triangles Class 9th Notes - Free NCERT Class 9th Maths Chapter 7 Notes - Download PDF

# Triangles Class 9th Notes - Free NCERT Class 9th Maths Chapter 7 Notes - Download PDF

Edited By Ramraj Saini | Updated on Apr 21, 2022 02:05 PM IST

## Triangles class 9 notes:

Introduction
The Triangles are the NCERT chapter in which The comprehensive notes for the concept of triangles cover the following concepts in detail: congruency, congruence criteria such as SAS, SSS, ASA, AAS, RHS, and so on. The NCERT Class 9 Maths Chapter 7 Notes covers a brief outline of the chapter Triangles. The main topics covered are Congruent Triangles, Criteria of congruence, SSS Congruence Criteria, SAS Congruence Criteria, ASA Congruence Criteria, AAS Congruence Criteria, RHS Congruence Criteria, and many more concepts related to the Triangles in the Triangles class 9 notes with some FAQs.

The basic equations in the chapter are also covered in the class 9 maths chapter 7 notes. All of these subjects are covered in the Triangles class 9 notes pdf download. CBSE class 9 maths chapter 7 notes also contain important formulas. Notes for class 9 maths chapter 7 contains systematic explanations of topics using examples and exercises. This NCERT note includes FAQ’s or frequently asked questions about the chapter.

Also, students can refer,

NCERT Class 9 Maths Chapter 7 Notes

## Congruent Triangles

When all three corresponding sides and three corresponding angles of a pair of triangles are exactly equal, the triangles are said to be congruent.

The corresponding parts of congruent triangles are equal and are denoted as CPCT ( The corresponding part of the congruent triangle ).

## Criteria For Congruence

The congruency of the triangles is determined by the criteria listed below.

SSS Congruence Criteria

The two triangles are said to be congruent when the three sides of one triangle equal the three sides of the other.

If all sides are the same, the angles that correspond to them must likewise be the same.

SAS Congruence Criteria

Axiom: Two triangles are congruent if their two sides and included angle are equivalent to the other triangle's corresponding sides and included angle.

ASA Congruence Criteria
Two triangles are congruent if one triangle's two angles and included side are equivalent to the other triangle's corresponding two angles and included side.

AAS Congruence Criteria

Two triangles are said to be congruent if two angles and one side of one are equivalent to two angles and one side of the other.

## Why Are The SSA And AAA Congruence Rules Invalid?

Because the angle is not included between the pairs of equal sides, the SSA or ASS test is not a viable test for congruency.

The AAA test is likewise invalid because, while two triangles can have the same three angles, their sides can be of different lengths.

This becomes a similarity test (AA).

RHS Congruence Criteria

When the hypotenuse and one side of one right triangle equals the hypotenuse and one side of the other, the two triangles are said to be congruent.
Right angle – Hypotenuse – Side is abbreviated as RHS.

## Isosceles Triangle Properties

When two triangle sides are equal, the angles opposite those sides are equal as well, and vice versa.

Congruence of Triangles Criteria

The following are the conditions for triangle congruence:
SAS
ASA
AAS
SSS
RHS
It is written as ΔABC ≅ ΔXYZ

## Triangles With Inequalities

The relationship between the triangle's uneven sides and the angles on the opposite side.
When the angles opposite the longer and shorter sides of a triangle are unequal, the angle opposite the longer side is larger than the angle against the shorter side.

Inequality In The Triangle

The lengths of any two sides of a triangle must add up to more than the length of the third side.

## Significance of NCERT class 9 maths chapter 7 notes

This NCERT class 9 maths chapter 7 will help students to understand the formulas, statements, and rules in detail.

Class 9 mathematics chapter 7 notes pdf download can be used to prepare in offline mode.

NCERT solutions of class 9 subject wise

NCERT Class 9 Exemplar Solutions for Other Subjects:

NCERT Class 9 Notes Chapter wise

 NCERT Class 9th Math Chapter 1 Notes NCERT Class 9th Maths Chapter 2 Notes NCERT Class 9th Maths Chapter 3 Notes NCERT Class 9th Maths Chapter 4 Notes NCERT Class 9th Maths Chapter 5 Notes NCERT Class 9th Maths Chapter 6 Notes NCERT Class 9th Maths Chapter 7 Notes NCERT Class 9th Maths Chapter 8 Notes NCERT Class 9th Maths Chapter 9 Notes NCERT Class 9th Maths Chapter 10 Notes NCERT Class 9th Maths Chapter 11 Notes NCERT Class 9th Maths Chapter 12 Notes NCERT Class 9th Maths Chapter 13 Notes NCERT Class 9th Maths Chapter 14 Notes NCERT Class 9th Maths Chapter 15 Notes

1. What are Congruent Triangle according to class 9 Triangles notes?

Congruent Triangles

When all three corresponding sides and three corresponding angles of a pair of triangles are exactly equal, the triangles are said to be congruent.

The corresponding parts of congruent triangles are equal and are denoted as CPCT (The corresponding part of the congruent triangle ).

2. Write three equalities of similar angles if ∆SKY ≅ ∆MON by the SSS congruence rule.

Since ∆SKY ≅ ∆MON  follows the SSS congruence rule, three equivalent angle equalities are ∠S = ∠M, ∠K = ∠O and ∠Y = ∠N

3. If ∠N = 90 degrees in ∆MNO, write the longest side.

We already know that the side opposite the biggest angle is the longest.

∴ MO is the longest side.

4. What is the area of the triangle?

The area of a triangle is A = ( 1/2 ) b x h, where b is the breadth, h is the height

5. How useful are these class 9th maths chapter 7 notes for the CBSE board exam?

From the notes for class 9 maths chapter 7, students should expect 4 to 6 mark problems, and they can use these notes for a quick review to help them improve their grades.

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