RS Aggarwal Class 9 Chapter 8 Solutions (Triangles)
RS Aggarwal Solutions for Class 9 Maths Chapter 8 – Triangles will help you prepare better for the CBSE exam. In this chapter of RS Aggarwal Class 9 Maths Solutions, we will cover a total of 41 problems which are divided into 2 sections. You will learn about different concepts and Problems based triangles which are divided on the idea of the variety of sides and angles it possesses. Different styles of triangles based totally on the variety of sides are scalene triangles, Isosceles triangles, Equilateral triangles and the triangles based totally at the angles are Obtuse angled triangle, Acute angled triangle and Right-angled triangle.
RS Aggarwal Class 9 Maths Solutions for Chapter 8 – Triangles by instasolv sets a standard for comprehensive preparation and answers all the questions which may appear in the exam, regardless of their level of difficulty.
Instasolv’s R S Aggarwal solutions for Chapter 8 – Triangles help clarify your basic understanding of this chapter because there is a probability of higher scoring questions in this chapter. These RS Aggarwal problems with solutions can be referred for the final exam preparation. Solving exercise-related problems on a daily basis helps you to improve your problem-solving skills.
Important Topics for RS Aggarwal Solutions for Class 9 Maths Chapter 8 – Triangles
- In this topic you will learn about the basic concept of Triangle and its sides: the triangle is an enclosed figure which is formed by 3 intersecting lines i.e., three sides, three angles as well as three vertices.
- Below you can see the shape of a triangle:
- ABC named triangle will be denoted by symbolic representation: ∆ ABC. However, ∆ ABC has three sides AB, BC, CA, three angles ∠ A, ∠ B, ∠ C and three vertices A, B, C.
This chapter also includes some very important theorems i.e,
- Congruence of Triangles: The word ‘congruent’ means identical in all factors of the figures whose styles and sizes are the same.
For triangles, if the perimeters and angles of 1 triangle are equal to the corresponding facets and angles of the alternative triangle then they’re said to be congruent triangles.CPCTC is a short form for Corresponding Parts of Congruent Triangles.
Next topic to be considered will be the Criteria for Congruence of Triangles:
- SAS Congruence Rule:
Definition: Two triangles are congruent only if two sides, as well as the included angle of one triangle, are always equal to the sides and the included angle of the other triangle.
Taking an example: Provide Δ AOD ≅ Δ BOC
OA = OB and OC = OD
alongside ∠ AOD and ∠ BOC form a pair of vertically opposite angles,
∠ AOD = ∠ BOC
However, two sides and an included angle of a triangle are always equal, by SAS congruence rule, so we can say that Δ AOD ≅ Δ BOC.
- ASA Congruence Rule:
Definition: Two triangles are congruent only if two angles, as well as the included side of one triangle, is equal to two angles and the included side of another triangle.
Prove: Suppose there are two triangles ABC and DEF, such that ∠ B = ∠ E, ∠ C = ∠ F, and BC = EF.
Now, we need to prove that Δ ABC ≅ Δ DEF then:
If, AB = DE
From this assumption, AB = DE and given that ∠ B = ∠ E, BC = EF, so we can say that Δ ABC ≅ Δ DEF as per the SAS rule.
- Let us take: AB > DE or AB < DE
Let us take a point P on AB such that PB = DE as mentioned in the above figure. Now, from the assumption, PB = DE and given that ∠ B = ∠ E, BC = EF, we can say that Δ PBC ≅ Δ DEF as per the SAS rule.
Now, triangles are congruent, their corresponding parts will be equal.
Hence, ∠ PCB = ∠DFE
and it’s given that ∠ ACB = ∠ DFE, which confirms that ∠ ACB = ∠PCB
It can be possible only if “P” and “A are the same points or BA = ED.
Thus, Δ ABC ≅ Δ DEF as per “SAS rule”.
Similarly, for AB < DE, it can be proved that Δ ABC ≅ Δ DEF.
- Another important topic will be the Properties of a Triangle:
1st Theorem: It is defined as the Angles opposite to equal sides of an isosceles triangle are equal.
Proof: Suppose we are given isosceles triangle ABC having AB = AC.
We need to prove that ∠ B = ∠C
Firstly, we will draw a bisector of ∠ A which intersects BC at point D.
for the Δ BAD and Δ CAD, given that AB = AC, from the figure ∠ BAD = ∠ CAD and AD = AD.
Thus, by SAS rule Δ BAD ≅ Δ CAD.
Therefore, ∠ ABD = ∠ ACD, since they are corresponding angles of congruent triangles.
Hence, ∠ B = ∠C.
2nd Theorem: The sides opposite to equal angles of a triangle are equal.
- Criteria for Congruence of Triangles:
- As per SSS Congruence Rule:
If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
- Inequalities in a Triangle:
1st Theorem: If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater).
2nd Theorem: In any triangle, the side opposite to the larger (greater) angle is longer.
3rd Theorem: The sum of any two sides of a triangle is greater than the third side.
Exercise Discussion of Important Topics RS Aggarwal Solutions for Class 9 Maths Chapter 8 – Triangles
- The first section of Chapter 8 essentially contains 29 questions that will ask you to solve problems related to the total angles of triangles. This section will also ask you to find the value of “x” in the given diagrams of triangles.
- The second section of Chapter 8 will be MCQs having 12 questions that will ask you to choose correct answers by applying different theorems and concepts learned in this chapter.
- Instasolv RS Aggarwal Maths Solutions for Class 9 Chapter 8 will help you to revise the whole chapter in less time. The solutions are prepared in a stepwise manner to provide an effortless and better understanding of the concepts.
Why Use RS Aggarwal Solutions for Class 9 Maths Chapter 8 by Instasolv?
RS Aggarwal Solutions for chapter 8 is a wonderful source for students of 9th grade to clear the difficult concepts and improve each chapter by solving different questions.
Solving these RS Aggarwal questions enhances your problem-solving skills by giving students a clear and concise way of responding.
Students can learn to capture different ideas and formulas effectively and also manage their time effectively.