Question

State and prove Pythagoras theorem​

Answer 1

$\tt\pink{《ANSWER》}$

• 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 .

example:-

hypotenuse = 10cm

and the two sides are 6cm and y

to find use pythogoras theorem

10=6+y

y=10-6 [by Pythagoras theorem]

y=4cm

Answer 2

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.

Explanation:

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, AB AD= AC AB

Now, AB ²

=AD×AC ..........(1)

Similarly,

BC² =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 [hence proved]