RS Aggarwal Class 10 Solutions - Triangles

We have provided step by step solutions for all Exercise questions given in the PDF of Class 10 RS Aggarwal Chapter 4 - Triangles. All the Exercise questions with solutions in Chapter 4 - Triangles are given below:

Exercise (Ex 4A) 4.1

Exercise (Ex 4B) 4.2

Exercise (Ex 4C) 4.3

Class 10 Chapter 4: Triangles

As kids, we see numerous shapes in our surroundings in day to day life. However, we never really cared to discover more about the properties of these shapes. Hence, we learn about all these properties as we progress through higher school. Triangles are one of the most common shapes we've been seeing in our surroundings. In our portions, we study Triangles in-depth and understand every little aspect of them.

Important Points RS Aggarwal Solutions Class 10 Chapter 4 Triangles

There are three different types of Triangles when segregated based on angles within a Triangle, 

• Acute Triangle: An acute Triangle is a Triangle where each of the angles within a Triangle is less than 90 degrees, implies that the measure of each angle within the Triangle is less than 90 degrees

• Obtuse Triangle: An obtuse Triangle is a Triangle wherein the measure of at least one angle of the Triangle exceeds 90 degrees

• Right Triangle: A right-angled Triangle is a Triangle in which at least one of the angles of the Triangle is equal to 90 degrees.

Based on the lengths of the sides of a Triangle, there are three kinds as well:

• An isosceles Triangle is a special variety of Triangle in which two sides of the Triangle are equal and two angles are equal as well.

• A right Isosceles Triangle is a Triangle in which two angles of the Triangle are equal to 45 degrees and one angle is equal to 90 degrees.

• An equilateral Triangle is a Triangle in which each of the sides is equal and all the angles are equal to 60 degrees.

Pythagoras Theorem: The Pythagoras theorem is one of the most important theorems in right-angled Triangles. It is a very useful theorem to approach problems of Class 10 Chapter 4 Triangles. The theorem states that the square of the length of the longest side, that is the hypotenuse, will be equal to the sum of squares of the lengths of the other two sides.

Median of a Triangle: The medians of a Triangle are the line segments drawn from one vertex to the midpoint of the opposite side. 

Centroid: The point of intersection of all the medians is called the centroid of the Triangle. Interestingly the centroid of the Triangle also divides each median in a ratio of 2:1.

Altitude: Altitudes of a Triangle are the line segments drawn from the vertices of the Triangles to the side opposite to the Triangle such that the line segment makes a right angle with the side it intersects.

Orthocentre: The orthocenter is the point of intersection of all the altitudes within a Triangle.

Angular Bisectors: The line segment bisecting each angle of a Triangle and meeting the opposite side is called an angular bisector of the Triangle.

Incentre: The incentre of a Triangle is the point of intersection of all the angular bisectors of the Triangle.

• Interestingly, in an equilateral Triangle, the median, the altitude, and the angular bisectors are the same, and hence all the points, incentre, orthocentre and centroid are concurrent to each other.

• The sum of all the internal angles of a Triangle is always equal to 180 degrees.

• The sum of lengths of two sides is always greater than the length of the third side of the Triangle.

Heron's Formula: A formula to find the area of any Triangle by just knowing the length of each side of a Triangle.

s(semiperimeter):(a+b+c)/2

Where a,b,c are the lengths of sides of the Triangle respectively.

Area = √s(s–a)(s–b)(s–c)

Area of Triangle: ½*b*h where b is the base of the Triangle and h is the height or the altitude of the Triangle.

Area of an Isosceles Triangle:

A = (1/4) × b × √(4a2 – b2)

Where b is the length of the unequal sides of the Triangle and a is the length of sides that are equal.

Area of an Equilateral Triangle

Area of Equilateral Triangle = √3a2/4

Where a is the length of a side of the Triangle

Preparation Tips

While preparing for the topic Triangles, you must ensure to be thorough with all the important theorems and formulae. While solving the problems you need to implement the right property at the right place. This will make your problem solving much simpler. Following Vedantu solutions to RS Aggarwal will make your problem solving more systematic and simple!

Importance of learning CBSE Class 10 Maths Chapter 4- Triangles

• Triangles is an important Chapter as we learn about its different properties which will come in handy in the future Classes

• Triangles form the very basis of some of the important theorems

• Trigonometry becomes easier to understand

• Complex calculations become much easier if one properly learns about Triangles

• Areas such as Engineering, Astronomy,  Physics and Navigation become smoother to understand

• Unknown quantities in geometry can be easily determined

• Concepts of Euclid’s Geometry also becomes easier