Question

state and prove the pythagores theorem​

Answer 1

Answer:

Pythagoras theorem states that “ In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”. The sides of the right-angled triangle are called base, perpendicular and hypotenuse . Proof: ∠BAD = ∠BAC i.e. ∠A is common in both triangles.

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, AD/AB = AB/ AC

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]