Question

state and prove Pythagoras theorem​

Answer 1

Step-by-step explanation:

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

Given: ABC is a triangle in which ∠ABC=90⁰

Construction: Draw BD⊥AC.

Proof:

In △ADB and △ABC

∠A=∠A [Common angle]

∠ADB=∠ABC [Each 90⁰]

△ADB∼△ABC [A−A Criteria]

So, AD / AB = AC / AB

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.

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