Question

State and prove pythagoras theorem ​

Answer 1

Answer:

Statement: In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given: ABC is a triangle in which ∠ABC=90∘

Construction: Draw BD⊥AC.

Proof:

In △ADB and △ABC

∠A=∠A              [Common angle]

∠ADB=∠ABC      [Each 90∘]

△ADB∼△ABC    [A−A Criteria]

So, ABAD=ACAB

Now, AB2=AD×AC             ..........(1)

Similarly,

BC2=CD×AC               ..........(2)

Adding equations (1) and (2) we get,

AB2+BC2=AD×AC+CD×AC

=AC(AD+CD)

=AC×AC

∴AB2+BC2=AC2 [henceproved]

Answer 2

Step-by-step explanation:

i hope it's helpful for you