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In a triangle, if square of …

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In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then prove that the angle opposite to the first side is a right angle.
  • 1 answers

Gaurav Seth 5 years, 1 month ago

 

Q: Prove that in a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

A n s w e r :

Given: A triangle ABC in which AC2 = AB2 + BC2.
To Prove: ∠B = 90°.
Construction: We construct a ΔPQR right-angled at Q such that
PQ = AB and QR = BC
Proof: Now, from ΔPQR, we have,

Now, in ΔABC and ΔPQR,

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