State and proove "Pythagoras Theorem " by using the concept of similarity of triangles .
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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,
AB
AD
=
AC
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
[henceproved]
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