RD Sharma Class 9 Chapter 10 Solutions (Congruent Triangles)

RD Sharma Class 9 Maths Solutions for Chapter 10 have been prepared with the viewpoint to provide you with the right guidance in understanding the concepts in the congruent triangles. The topics covered in this chapter will help you gain clarity about the congruence of line segments, congruence of angles, and more complex subject of congruence in triangles. Hence, you will get to learn about congruence relations and inequality theorems in a triangle. The weightage of this chapter of RD Sharma Solutions in the school exams is very significant. Regular and consistent practice of the exercises will help you get maximum marks from this chapter.

There are 22 questions in this chapter compiled systematically in 6 exercises and additional VSAQs exercises consisting of 6 questions. The exercises are based on all the criteria of congruence of triangles separately. The inequality relations of triangles and theorems related to the median in a triangle are all covered in these exercises. The questions will require an in-depth knowledge of all the axioms and theorem studied in the previous chapters such as lines and angles, and triangle and its properties. You will get to prove various important results besides getting to find the congruent triangles.

Instasolv experts are dedicated to figuring out your requirements from your digital guide and therefore, we will not leave any of your queries unaddressed. The answer to each question is discussed in detail with the explanation of the solutions in a step by step manner. The expert team of Instasolv has used its experience in writing this set of answers to make sure that these are in total compliance with the CBSE guidelines. Solving these questions with our assistance will help you achieve good grades in your school exams.

Important Topics for RD Sharma Solutions for Class 9 Chapter 10: Congruent Triangles

Introduction to Congruence

  1. Congruence: The figures which have equal shapes and sizes or are equal in all perspectives.
  2. A number of examples can be spotted where congruence of figures (straight lines or angles also) is used from our daily life situations, such as whenever identical objects are manufactured, the casts are made congruent.
  3. Two given triangles under consideration are congruent if the sides and angles of both the triangles are equal to one another’s corresponding sides and angles.
  4. Corresponding Parts of Congruent Triangles: In two given congruent triangles, the corresponding parts are equal. We use the abbreviation CPCT for such parts.

SAS Congruence Rule:

The SAS Congruence rule is an axiom. Following this rule, If in two triangles, the triangles have the corresponding pairs of two sides and the included angles between them equal, then the two triangles are congruent.

Note: SAS congruence rule is correct but not ASS or SSA rule.

ASA Congruence Rule:

If in two triangles, the triangles have the corresponding pairs of two angles and the included side between them equal, then the two triangles are said to be congruent.

Also, the AAS Congruence rule is correct if two pairs of angles and any one pair of corresponding sides, in the given two triangles are equal.

SSS Congruence Rule:

Two triangles will be congruent if all the sides of one triangle are equal to all the corresponding sides of another triangle by the SSS Congruence rule. This theorem can be proved by combining the above results.

RHS Congruence Rule:

If the hypotenuse and one side of one of the two given right-angle triangles happen to be equal to the hypotenuse and one side of another right-angled triangle, then these two right-angled triangles are said to be congruent. RHS is the abbreviation that we use for the criteria “Right Angle, hypotenuse, and side”.

Inequalities in a Triangle:

The relation between the unequal sides and unequal angles of a triangle can be described by the following points:

  1. The largest side of the triangle has the greatest angle opposite to it in the triangle under consideration.
  2. The largest angle has the largest side opposite to it in any given triangle.
  3. The sum of any two sides of a given triangle is always found to be greater than the length of the third side of the triangle.

Exercise Discussion for RD Sharma Solutions for Class 9 Chapter 10: Congruent Triangles

  1. The 6 exercises in this chapter are based separately on each congruence criteria and the inequality theorems of triangles.
  2. Exercise 6.1 is based on the SAS criterion of congruence of triangles. You will also be required to prove lines as parallel to one another using the theorems learnt in lines and angles.
  3. The questions in exercise 6.2 are based on the ASA or AAS congruence rule. There are 3 questions in this exercise in which you will also get to use the properties of an isosceles triangle.
  4. The questions in exercise 6.3 will require you to apply the RHS congruence criterion to prove the given right-angled triangles as equal.
  5. In the problems given in 6.4, you will get to apply the side side side congruence criterion to prove the given triangles as congruent. There is also extensive use of the property ‘corresponding parts of congruent triangles’
  6. Exercise 6.5 is an application of the theorems related to properties of the isosceles triangles and right-angled triangles.
  7. Lastly, 6.6 employs the angle sum property and other theorems of inequalities in triangles.
  8. VSAQs exercise consists of small answer type theorem based questions, which may be of any of the 4 congruence criteria.

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