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## NCERT Solutions for Class 10 Maths Chapter 6 Exercise 6.4

Class: 10 | Maths (English and Hindi Medium) |

Chapter 6: | Exercise 6.4 |

### 10 Maths Chapter 6 Exercise 6.4 Solutions

NCERT Solutions for Class 10 Maths Chapter 6 Exercise 6.4 Triangles in English medium as well as Hindi Medium free to use online or download in PDF updated for academic session 2022-23 for High School students. Move Class 10 Maths Chapter 6 main page for other exercises to download or online study. Join the Discussion Forum to ask your doubts and response to other’s questions. Vedic Maths is important tools for class 10 students to make calculation easier and faster.

#### Class 10 Maths Chapter 6 Exercise 6.4 Solution in Hindi Medium

#### Class 10 Maths Chapter 6 Exercise 6.4 Solution in Videos

### Important Questions of 10th Maths exercise 6.4

### What is Area Theorem in class 10?

The ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides. [This also known as Area Theorem. In this theorem, the ratio of area is equal to square of corresponding sides but ratio is also equal to the corresponding altitudes, median.]

### How many theorems are there in chapter 6, which may be asked to prove?

There are four theorems in class 6 which are asked to prove:

1. BPT or Thales Theorem

2. Area Theorem

3. Pythagoras Theorem

4. Converse of Pythagoras Theorem

#### About 10 Maths Exercise 6.4

In Exercise 6.4, mainly we have to solve the questions based on ratio of area of similar triangles with their corresponding sides, perimeters, altitudes, medians, etc. In Exercise 6.3, we have learnt that if triangles are similar then their sides are proportional. Here, we have to relate it from area also.

##### Extra Questions on Similar Triangles

In triangle ABC, If AD is the median, Show that AB² + AC² = 2(AD² + BD²)

In triangle ABC, angle C is a right angle. Points P & Q lies on the sides CA & CB respectively. Prove that AQ² + BP² = AB² + PQ²

If AD and PS are medians of angle ABC and angle PQR respectively where angle ABC ~ angle PQR, Prove that AB/PQ = AD/PS.

In an equilateral angle ABC, AD is perpendicular to BC, Prove that 3AB² = 4AD².

Prove that the sum of the square of the sides of a rhombus is equal to the sum of the squares of its diagonals.

### How many questions are there in exercise 6.4 of class 10th Maths?

There is only 1 example (Example 9) and 9 questions in exercise 6.4 of class 10th Math.

### Is exercise 6.4 of class 10th mathematics based on theorems?

Yes, Exercise 6.4 of class 10th mathematics based on Theorem 6.6 (The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides).

### How much time students need to complete exercise 6.4 of class 10th math?

Students need at least 3 days to complete exercise 6.4 of class 10th math. Also this time depends on student’s speed and capability.

### Which question of class 10 Maths Exercise 6.4 is based on theorem 6.6?

Let ∆ ABC ~ ∆ DEF and their areas be, respectively, 64 cm² and 121 cm². If EF = 15.4 cm, find BC.