Question

Prove Pythagoras theorem with proper diagram. How square of the hypotenuse is equal to the sum of the

square of the other two sides.​

Answer 1

Answer:

Step-by-step explanation:

Pythagoras Theorem Proof

The proof of Pythagorean Theorem is provided below:

Let us consider the right-angled triangle △ABC wherein ∠B is the right angle (refer to image 1).

In order to prove (AB)2 + (BC)2 = (AC)2, let’s draw a perpendicular line from the vertex B (bearing the right angle) to the side opposite to it, AC (the hypotenuse), i.e. BO ⊥ AC.

Now, in △ABC and △ABO, we have:

i) ∠A is common.ii) ∠AOB = ∠ABC (Both are 90°)

Therefore, △ABC ~ △ABO (By AA-similarity)

So, AO/AB = AB/AC.

=> (AB)2 = AO × AC ——– (1)

Now, in △ABC and △OBC, we have:

i) ∠C is common.ii) ∠BOC = ∠ABC (Both are 90°)

Therefore, △ABC ~ △OBC (By AA-similarity)

So, OC/BC = BC/AC.

=> (BC)2 = OC × AC ——– (2)

Adding equation 1 and equation 2, we have:

(AB)2 + (BC)2 = AO × AC + OC × AC

=> (AB)2 + (BC)2 = AC (AO + OC)

=> (AB)2 + (BC)2 = AC × AC (Now, since AO + OC = AC)

=> (AB)2 + (BC)2 = (AC)2

Hence, the Pythagorean Theorem is proved.

Answer 2

Answer:

pythagoras therom states that= a²+b²=c²

Step-by-step explanation:

hypotenus is the longest side and it is the sum of the other two sides