Question

write and prove the Pythagoras theorem​

Answer 1

Answer:

h^2=p^2+b^2

Step-by-step explanation:

According to pythagoras theorem, the square of hypotenuse is equal to the sum of square of perpendicular and square of base in any right angled triangle.

i.e. h^2=p^2+b^2

Answer 2

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 [hence proved]