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RS Aggarwal Class 10 Chapter 7 Solutions (Triangles)

RS Aggarwal Solutions for Class 10 Maths Chapter 7 ‘Triangles’ that will help you solve all the exercises of the chapter easily. In this chapter of RS Aggarwal Class 10 Maths Solutions, there are 186 questions divided into 5 exercises. You shall learn how to solve unique problems based on triangles and vital theorems. The main topics of the chapter are congruent figures, similar figures and similar Polygons. This chapter will clear all your doubts upon equilateral triangles and similar triangles and will give an explanation for ideas of similarity of triangles in addition to the ratio of the areas of two similar triangles.

The solutions of the chapter created by our subject matter experts will immensely improve your concept-based knowledge. The exercise questions of the chapter include concepts like finding the base of the triangle when other sides are given. There are questions based on angle bisectors, parallel lines within triangles, finding angles in a triangle when two similar triangles are given, finding the length of median of a triangle when its area is given, finding altitude of isosceles triangles, and the Pythagoras theorem. 

The RS Aggarwal Solutions for Chapter 7 of Class 10 book is provided in a stepwise manner for you. These solutions will help as a guide for solving the exercises of the chapter. The extensive explanations of the theorems used in this chapter will help you prepare this chapter efficiently for Class 10 board exams. 

Important Topics for RS Aggarwal Solutions for Class 10 Maths Chapter 7 –Triangles

Triangle

  • A triangle is said to be a polygon that has 3 angles along with 3 sides. 
  • A triangle always has interior angles as 180 degrees and exterior angles of 360 degrees. Based on different angles of triangles and its corresponding length, they can be categorized under the following types:
    • Scalene Triangle – such triangles have 3 sides different measures.
    • Isosceles Triangle is the triangle with 2 sides of equal length.
    • Equilateral Triangle is the triangle with 3 sides that are equal with interior angles 60 degrees.
    • The Acute angled Triangle is the triangle with smaller angles at 90 degrees.
    • Right angle Triangle is the triangle having a single 90 degrees angle.
    • Obtuse-angled Triangle is a triangle with an angle bigger than 90 degrees.

Criteria of Similarity of Triangles

  • Side-Side- Side (SSS) identical Criterion – When the corresponding sides of any two triangles are in the equal ratio, then their corresponding angles can be identified and the triangle could be considered as comparable triangles.
  • Angle- Angle -Angle (AAA) identical Criterion – When the corresponding angles of any two triangles are identical, then their corresponding side might be in the equal ratio and the triangles are considered to be the same.
  • Angle-Angle (AA) identical Criterion – When two angles of 1 triangle are respectively equal to the 2 angles of the opposite triangle, then the two triangles are considered as similar. 
  • Side-Angle-Side (SAS) identical Criterion – When one angle of a triangle is identical to one attitude of any other triangle and the sides together with these angles are in the identical ratio (proportional), then the triangles are said to be same.

Pythagoras Theorem

Definition: In a right-angled triangle, the sum of squares of two sides of the right triangle is identical to the square of the hypotenuse of the triangle.

Theorem: If a line divides any two sides of a triangle in the same ratio, then the line is said to be parallel to the third side.

Let us take ABC to be a triangle with sides as AB, AC, and BC.  Where DE is divided into two sides of the triangle within the same ratio.

Given: Line of the triangles divided into the same ratio. Thus,

ADDB = AEEC

Proof:

ADDB = AEEC (Given)—-(1)

Let us assume that DE is not parallel to BC. Now we draw DE’ which is assumed to be parallel to BC. So,

ADDB = AE′E′C (a property of identical triangles)—-(2)

Therefore, from (1) and (2)

AEEC = AE′E′C

Now we will add 1to both sides,

AEEC + 1 = AE′E′C + 1

⇒ AEEC + ECEC = AE′E′C + E′CE′C

⇒ AE + ECEC = AE′+E′CE′C

As per the figure given above, AE+EC = AC and AE′+E′C = AC, now applying these values in the equation above:

ACEC = ACE′C

This directly confirms that EC = E′C and E = E′ meaning that they are the identical point.

Hence DE is said to be parallel to BC. Hence, proving the similarity of triangles.

Basic Proportionality Theorem 

  • This theorem was brought through a famous Greek Mathematician, Thales, hence it’s also known as the Thales Theorem. 
  • According to him, for any equiangular triangles, the ratio of any two corresponding sides is constantly the same. Based on this concept, he gave a theorem of basic proportionality. 
  • This idea has been delivered in similar triangles. If two triangles are similar to every other then,
    • Corresponding angles of both triangles are equal.
    • Corresponding sides of each triangle are in share with each side.
    • If a line is drawn parallel to one side of a triangle intersecting the other aspects in distinct points, then the other lines are divided into identical ratios.

Exercise discussion for RS Aggarwal solution for class 10 chapter 7 –Triangles

Exercise 7A 

It has 13 questions that will ask you to solve various problems based on congruent figures, similar polygons, equiangular triangles, similar triangles. This exercise will also help you to understand some Important Theorems on Triangles.

Exercise 7B 

It has 19 questions which mainly focus on the several criteria for the similarity between two triangles as in the case of AAA, AA, SSS, and SAS similarity. 

Exercise 7C 

It contains 13 questions based totally on the ratio of the regions of two comparable triangles. The ratio of the areas of similar triangles is the same as the ratio of the square of their corresponding sides. 

Exercise 7D 

It contains 22 questions that mainly focus on Pythagoras Theorem and some important results based upon this theorem. Instasolv can help you with any type of questions related to these exercises.

Exercise 7E 

The fifth exercise of this chapter has 30 questions that are mainly based on Thales’ Theorem and its converse, Midpoint theorem and Similarity of two triangles along with results. At the end of the chapter, there are 54 multiple-choice questions based on all the miscellaneous concepts of the chapter. 

Why Use RS Aggarwal Solution for Class 10 Maths Chapter 7- Triangles by Instasolv?

  • Class 10 Maths Chapter 7 RS Aggarwal Solutions will help you revise the entire chapter in less time. 
  • You will be able to analyze your flaws and solve conceptual-based problems.
  • Our RS Aggarwal Solutions provide answers to all the exercises of the chapter with a proper approach solving the problems. 
  • These solutions can help clear your doubts about concepts and you can easily analyze your weak areas of the chapter.