Question

स्टेट एंड प्रोव फंडामेंटल थिअरी ऑफ पाइथागोरस क्लास 10th ​

Answer 1

Step-by-step explanation:

the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

Answer 2

Answer:

The Pythagoras theorem, also known as the Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle. Or, the sum of the squares of the two legs of a right triangle is equal to the square of its hypotenuse.

Let us call one of the legs on which the triangle rests as its base. The side opposite to the right angle is its hypotenuse, as we already know. The remaining side is called the perpendicular. So, mathematically, we represent the Pythagoras theorem as:

Hypotenuse2  =  Perpendicular2 + Base2 

Pythagorean Theorem Derivation

Consider a right-angled triangle ΔABC. From the below figure, it is right-angled at B.

From the above-given figure, consider the  ΔABC and ΔADB,

In  ΔABC and ΔADB,

∠ABC = ∠ADB = 90°

  ∠A = ∠A → common

Using the AA criterion for the similarity of triangles, 

ΔABC ~ ΔADB 

Therefore, AD/AB = AB/AC

⇒ AB2 = AC x AD  ……(1)

Considering  ΔABC and ΔBDC from the below figure.