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## Class 7 Maths Chapter 6 Exercise 6.4 Solution

### CBSE NCERT Class 7 Maths Chapter 6 Exercise 6.4 Solution in Hindi and English Medium

Class: 7 | Mathematics |

Chapter: 6 | Triangles and its Properties |

Exercise: 6.4 | PDF and Videos Solution |

### Class 7 Maths Chapter 6 Exercise 6.4 Solution in Videos

#### Pythagoras

Pythagoras was an eminent Greek philosopher who was born in 580 BC and died in 500 BC. He gave a wonderful relation between the lengths of the sides of a right triangle, which is known as Pythagoras theorem.

#### Pythagoras’ Theorem:

In a right angled triangle has one of its angles equals to 90°. The side opposite to the right angle is called the hypotenuse. The other two sides that contain right angle are called the base and perpendicular of the right angled triangle.

Thus, in a right triangle ABC in which ∠C = 90°,

we have: AB2 = BC2 + AC2 .

Thus, if AB = c, BC = a and AC = b,

we have: c2 = a2 + b2

In order to verify the above result, we perform the experiment given below.

(Hypotenuse)2 = (Base)2 + (Perpendicular)2

Thus, Pythagoras theorem states that, “In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of base and perpendicular.”

Remark: The two sides of a right triangle other than the hypotenuse are called its legs.

#### Converse of Pythagoras’ Theorem

If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is right-angled triangle.

Thus, in a triangle ABC, if AB2 = BC2 + CA2, then the triangle is right-angled at C.

(i) Let a = 3 cm, b = 4 cm and c = 5 cm.

Then, 32 + 42 = 9 + 16 = 25 = 52

a2 + b2 = c2.

Now, draw triangle ABC such that BC = 3 cm, CA = 4 cm and AB = 5 cm.

Measure ∠C. You will find that ∠C = 90°.

So, triangle ABC is right-angled at C.

### Class 7 Maths Exercise 6.4 Important Questions

### How do you solve Pythagorean theorem questions?

Add the square of the two sides. If this sum is equal to the square of the hypotenuse, the triangle is right. If the two sides of the equation are not equal, the triangle is not right. Since the equation is not true, the triangle is not right.

### How is Pythagoras theorem proved?

The greater significance of Pythagoras’ Theorem is that it holds for all right-angled triangles, large or small — all infinitely many of them. Mathematical reasoning is powerful enough to cut through finite bounds; a single argument can qualify Pythagoras’ formula as true for every conceivable right-angled triangle.

### How do we use Pythagoras Theorem now a days?

The Pythagorean Theorem is useful for two-dimensional navigation. You can use it and two lengths to find the shortest distance. The distances north and west will be the two legs of the triangle, and the shortest line connecting them will be the diagonal. The same principles can be used for air navigation.

### Show that triangle ABC, is a right angle triangle if a = 6 cm, b = 8 cm and c = 10 cm.

Let a = 6 cm, b = 8 cm and c = 10 cm.

Then, 62 + 82 = 36 + 64 = 100 = (10)

Or, a2 + b2 = c2.

Now, draw triangle ABC such that BC = 6 cm, CA =8 cm and AB =10 cm.

Measure ∠C. You will find that ∠C = 90°.

So, triangle ABC is right-angled at C.