Concise Mathematics Class 9 ICSE Solutions for Chapter 10 - Triangle

Our experts at Vedantu design ICSE Selina Concise Solutions is a straightforward and precise format explaining all the necessary concepts included in the syllabus quite easily and effectively. These Selina solutions can help the students to get excellent marks in their exams. Proper study materials, easy and accurate solutions will help in the quick understanding of concepts. Experts at Vedantu have compiled all the essential concepts in an easy to understand format to make the last minute revision easier. The Vedantu ICSE Selina Solutions are prepared according to the updated ICSE syllabus.

Numerous examples present before the problems help students gain confidence in solving challenging problems on triangles, with ease.

Vedantu Selina Solutions for chapter 10 triangles will help students to understand the concepts of triangles, congruent triangles and various criteria for congruence. Students will also learn the inequality theorem of the triangle and its application in problems. Before jumping to solve the problems on triangles let us revise the important concepts of triangles.

Class 9 - Triangles

A figure that if formed by the intersection of three lines is said to be a triangle. It has three vertices, three sides, and three angles.

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In the above figure ABC is a triangle, and AB, BC, AC, are the sides of the triangle. A, B, C are the vertex and ∠ A, ∠B, ∠ C are the three angles.

Congruent Triangles

Two triangles are said to be congruent if the sides and angles of one triangle are exactly equal to the corresponding sides and angles of the other triangle.

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From the figure, △ABC is congruent to △DEF  and it is written as △ABC  ≌ △DEF

In two congruent triangles, corresponding parts of corresponding angles are congruent written as ‘c.p.c.t’ they are:

∠ A = ∠ D,

∠ B = ∠ E,

 ∠ C = ∠ F  

and

 AB = DE ,

 BC = EF ,

 AC = DF.

Note:

• Every triangle is congruent to itself.

• If △ABC  ≌ △DEF then DEF  ≌ △ABC

• If △ABC  ≌ △ DEF and DEF  ≅ △PQR then △ABC  ≅ △PQR

Criteria for Congruence of Triangles 

Different rules for congruence are as given below:

• SAS( Side-Angle-Side) Congruence Rule

If two sides and the angle included between the two sides of one triangle are equal to the corresponding sides and the included angle of the other triangle then the two triangles are congruent to each other.

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• ASA ( Angle-Side-Angle) Congruence Rule

If two angles and the side included by the two angles of one triangle are equal to the corresponding angles and side included by the angles of another triangle then the two triangles are said to be congruent. 

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• AAS (Angle-Angle-Side) Congruence Rule

If two angles and one non-included side of one triangle are equal to corresponding angles and a non-included side of another triangle then the two triangles are said to be congruent to each other.

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• SSS ( Side-Side-Side) Congruence Rule

If all the three sides of a triangle are equal to the corresponding sides of another triangle then the two triangles are said to be congruent to each other.

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• RHS( Right angle-Hypotenuse-Side) Congruence Rule

Two right-angled triangles are congruent if one side and the hypotenuse of the one triangle are equal to the corresponding side and the hypotenuse of the other.

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Inequality Relations In a Triangle

If two sides of a triangle are unequal, the longer side has a greater angle opposite to it, here if in △ABC, BC > AB. then ∠ CAB > ∠ ACB 

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• The Triangle Inequality Theorem States That

The sum of the lengths of any two sides of a triangle is greater than the length of the third side of a triangle.

Key Features of Vedantu Solutions 

The Vedantu Selina Maths Solutions are designed to give maximum information to students preparing for the ICSE class 9 examinations. The questions are answered in a step-by-step and easy to understand manner. By referring to Vedantu Solutions, students can grasp the concepts behind the solutions very quickly. This will not only aid students by giving them the confidence to answer all sorts of questions in the examinations but will also ensure that they learn the concepts in the long run as well. 

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• In-depth knowledge of the chapter is provided in easy language.

• Is based on the latest ICSE syllabus.

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• All the doubts that might arise while solving the exercise questions will vanish by going through these Vedantu Selina solutions

The Vedantu Selina Maths Class 9 Chapter 10 Triangle Solutions focuses on answering the questions in the right way to encourage students to fetch full marks in the examination.

All the Selina Maths Solutions are created by our experts who have vast academic experience.

ICSE Class 9 syllabus is vast and needs concentrated efforts on the part of the students to face the examinations and shine out successful. The Vedantu Selina Concise Maths Class 9 ICSE solutions pdf includes details for all chapters from the subject. This will allow the students to examine and understand every concept even if practising for the first time.

By studying these Selina ICSE Solutions for Class 9 you can easily get high marks in ICSE Class 9 Examinations.