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Pythagoras Theorem

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In DeltaABC , /_C is an acute angle, seg AD bot seg BC . Prove AB^(2)=BC^(2)+AC^(2)-2BCxxDC by completing the following activity. Let AB=c , AC=b , AD=p , BC=a , DC=x :.BD=a-x In DeltaADB , by Pythagoras theorem, c^(2)=(a-x)^(2)+square c^(2)=a^(2)-2ax+x^(2)+square ........... (1) In DeltaADC , by Pythagoras theorem, b^(2)=p^(2)+square p^(2)=b^(2)-square .......... (2) Substituting value of p^(2) from (2) in (1) c^(2)=a^(2)-2ax+x^(2)+square c^(2)=a^(2)+b^(2)-square :.AB^(2)=BC^(2)+AC^(2)-2BCxxDC .

Theorems

Theorems

(Pythagoras's Theorem) Prove by vector method that in a right angled triangle,the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Without using Pythagoras's theorem, show that the points A(1, 2), B(4, 5) and C(6, 3) are the vertices of a right-angled triangle.

Which of following does not form a Pythagoras triplet ?

Pythagoras was a student of