NCERT Solutions for Class 10 Maths Chapter 6 Ex 6.4

 

NCERT Solutions for Class 10 Maths Chapter 6 Ex 6.4 help you understand how to find areas of similar Triangles. Revising the questions of this exercise will help you prepare well for your Class 10 Maths board exam as per the latest exam pattern. The solutions are prepared by askIITians Maths experts with utmost clarity on the topic of areas of similar triangles. You can download these solutions in PDF form for free and refer to them as many times as you want. Given below are the details of this exercise so that you can understand what kind of questions are included in it. 

 

About NCERT Class 10 Maths Chapter 6 Triangles Ex 6.4

 

The NCERT Class 10 Maths Chapter 6 Triangles is based on the similarity of triangles. This chapter includes various theorems based on the similarity of triangles and areas of similar triangles that you must learn if you want to score full marks in this chapter. 

 

Exercise 6.4 of the Triangles chapter includes 9 questions that will help you master the theorem related to areas of similar triangles. According to this theorem:

 

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

 

In the given image: 

 

 

If ∆ABC ~ ∆PQR, then 

 

 

Types of questions included in NCERT Class 10 Maths Chapter 6 Ex 6.4:

 

Ex 6.4 Q1: In this question, you are given the areas of two similar triangles and you have to find the length of one of the sides. You are given that ∆ ABC ~ ∆ DEF and their areas are 64 cm2 and 121 cm2 respectively. If EF = 15.4 cm, find BC.

 

Ex 6.4 Q2: In this question, you are given that the diagonals of a trapezium ABCD with AB || DC intersect each other at the point O. If AB = 2 CD, find the ratio of the areas of triangles AOB and COD. You can find the stepwise solution to this question in our NCERT Solutions for this chapter. 

 

Ex 6.4 Q3: This question is based on a figure. In this question, you are given that ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, you have to show that ar (ABC)/ ar (DBC) = AO/ DO. 

 

Ex 6.4 Q4: In this question, you have to prove a theorem. If the areas of two similar triangles are equal, you have to prove that they are congruent.

 

Ex 6.4 Q5: D, E and F are respectively the mid-points of sides AB, BC and CA of ∆ ABC. Find the ratio of the areas of ∆ DEF and ∆ ABC. 

 

Ex 6.4 Q6: In this question, you have to prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

 

Ex 6.4 Q7: In this question, you have to prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.

 

Ex 6.4 Q8 and Q9: These are multiple-choice questions (MCQs) where you have to tick the correct answer and provide a justification for that answer. In question 8, you are given that ABC and BDE are two equilateral triangles such that D is the midpoint of BC. You have to find the ratio of the areas of triangles ABC and BDE. In question 9, you are given that sides of two similar triangles are in the ratio 4:9. You have to find the ratio of the areas of these triangles. 

Download Free NCERT Solutions for Class 10 Maths Chapter 6 Ex 6.4

 

As you can see, the exercise questions of Chapter 6 Ex 6.4 include questions where you have to give proper reasoning and also have to prove theorems. Students often find such questions difficult to handle. But with our NCERT Solutions for Class 10 Maths Chapter 6 Ex 6.4, you can master how to solve such questions in a stepwise manner and practice this exercise. 

 

Key features of NCERT Solutions for Class 10 Maths Chapter 6 Ex 6.4:

• The NCERT Solutions for Triangles chapter helps you master the concept of areas of two similar triangles. 
• These solutions include comprehensive explanations and easy-to-understand reasoning for every question. 
• The solutions of the exercise are solved step by step to bring full clarity about the topic of areas of similar triangles. 
• Our NCERT Solutions are free to download in Pdf form so that you can refer to them as many times as you want. 
• These solutions encourage independent learning amongst students as you can practice these solutions at your own pace. 

Download exercise-wise solutions for NCERT Class 10 Maths Chapter 6:

 

• NCERT Solutions for Class 10 Maths Chapter 6 Ex 6.1
• NCERT Solutions for Class 10 Maths Chapter 6 Ex 6.2
• NCERT Solutions for Class 10 Maths Chapter 6 Ex 6.3
• NCERT Solutions for Class 10 Maths Chapter 6 Ex 6.4
• NCERT Solutions for Class 10 Maths Chapter 6 Ex 6.5
• NCERT Solutions for Class 10 Maths Chapter 6 Ex 6.6

NCERT Class 10 Maths Chapter 6 Ex 6.4 FAQs

 

1. How many questions are there in exercise 6.4 of Class 10 Maths Chapter 6? 

Exercise 6.4 of the Triangles chapter includes 9 questions. 

 

2. Exercise 6.4 of Class 10 Maths is based on which theorem?

Exercise 6.4 is based on the following theorem: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

 

3. Why should I download the NCERT Solutions for Class 10 Maths Chapter 6 Ex 6.4 from askIITians? 

The exercise solutions for NCERT Class 10 Maths Chapter 6 Ex 6.4 are prepared by askIITians experts who have more than 15 years of online teaching experience. The solutions follow CBSE guidelines for exam patterns and syllabus as per the current academic session. They are easy to understand and a hundred per cent reliable.