Question

state and prove pythagoras theorem​

Answer 1

Step-by-step explanation:

here's your answer

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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]

$So,\frac{AD}{AB} = \frac{AB}{AB}$

Now,

${AB}^{2}$ =AD×AC ..........(1)

Similarly,

${BC}^{2}$=CD×AC ..........(2)

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

${AB}^{2} + {BC}^{2} = AD×AC+CD×AC$

=AC(AD+CD)

=AC×AC

$∴ {AB}^{2} + {BC}^{2} = {AC}^{2} </p><p> [hence proved]$